Washington (CNN) -- Whether political theater or sincere outreach, President Barack Obama's so-called charm offensive is part of what shapes up to be the first formal congressional budget debate since he took office four years ago.
Obama invited a dozen Senate Republicans to dinner and then hosted lunch at the White House with two House leaders last week. He will meet separately in coming days with House Republicans and Democrats as both parties begin unveiling their budget plans for the rest of this year and 2014.
Wary Republicans call the president's new outreach a good first step, but said the style must be matched by substance.
"I believe anytime both parties are talking it's a good thing," Rep. Kevin McCarthy of California told CNN on Sunday, adding: "Is this about politics, or is this genuine? Only time will tell."
House Budget Committee Chairman Paul Ryan of Wisconsin also said Sunday on Fox that Obama must change from the campaigner-in-chief who Republicans believe is only interested in promoting party goals.
"Will he resume attacking Republicans and impugning our motives? Will he resume what is long believed to be a plan to win the 2014 elections?" asked Ryan, the GOP vice-presidential nominee last year who took part in last week's White House lunch with the president.
"Or will he sincerely change and try and find common ground, try and work with Republicans to get something done? That's what we hope happens," he added.
To Rep. Debbie Wasserman Schultz of Florida, the chairwoman of the Democratic National Conference, rebuilding damaged relations is necessary on both sides for any progress to occur.
"There is a trust deficit and the way in my experience in 20 years as a legislator that you close that trust gap is to sit down and continue to talk," she told ABC on Sunday. "I'm a lot more likely to reach consensus and agree on the facts when I have spent some time getting to know, and working with, the other side."
The Republican-led House has passed a proposal to fund the government through September -- the end of the current fiscal year -- and Ryan will unveil his 2014 spending plan this week to kick off the congressional back-and-forth.
Meanwhile, Senate Democrats plan to detail their own proposals as soon as this week, and the White House was expected to bring out its budget plan next month.
"The president will outline again through the budget process his priorities -- economic priorities and policy priorities, both in deficit reduction and in economic growth and job creation," White House spokesman Jay Carney told reporters on Monday. "And his budget will contribute to the process of regular order that we hope will produce bipartisan, balanced deficit reduction."
By clearly staking out positions in the formal budgeting process, Obama and Congress appear intent on trying to avoid the crisis-driven brinksmanship of the past four years that deepened Washington's defining political divide.
During Obama's first term, House Republicans passed partisan budgets that Senate Democrats ignored, forcing the repeated extension of past spending plans.
Meanwhile, the president's budget proposals generated little support in Congress.
The upcoming negotiations are complicated by lingering fiscal issues from past showdowns.
Deep cuts to military and other discretionary spending took effect this month, and both sides were expected to try to soften their impact through the funding measure for the rest of 2013, which is called a continuing resolution. It must pass by March 27 to prevent a partial government shutdown.
Congress also must authorize an increase in the federal borrowing limit this summer.
Here are possible outcomes:
The Grand Bargain
A comprehensive deficit-reduction deal appeared close during Obama's first term, but eventually fell apart over the deep ideological differences regarding taxes.
Such an agreement would reform the tax system to lower both personal and corporate rates while eliminating some loopholes and breaks. It also would reform Medicare and Medicaid and possibly Social Security to ensure their solvency.
Republicans, especially conservatives, oppose any kind of increase in tax rates or revenue in their push to reduce the size of government. They also want to shrink the costs of entitlement programs that are the main drivers of chronic federal deficits and debt.
Democrats want to preserve the social safety net of entitlements for the elderly, poor and disabled, with Obama and party leaders insisting on more tax revenue as part of any deficit deal.
In winning re-election last year, Obama campaigned on protecting middle class Americans from the burden of deficit reduction, calling for the wealthy to contribute more in the form of increased tax revenue and other steps as part of entitlement reforms.
The major sticking point of a comprehensive agreement will be taxes. Obama and Democrats want to eliminate tax breaks and loopholes worth about $600 billion over 10 years as part of a broader $1.2 trillion deficit-reduction package that would include entitlement reforms.
Some Republicans have indicated support for ending such tax breaks as part of a broad deal. However, the fiscal-cliff agreement in January returned tax rates on top income earners to higher levels of the 1990s, and GOP leaders now oppose any further steps to raise rates or tax revenue.
A sticking point in a possible compromise on taxes would be whether increased revenue realized through reforms, such as eliminating existing loopholes, go towards holding down rates or reducing the deficit.
Meanwhile, Republicans say Obama and Democrats must deliver on significant entitlement reforms.
Sen. Rob Portman, R-Ohio, argued Sunday on CBS that Obama must use his profile to convince fellow Democrats and the American people that changes to Medicare and other entitlements are necessary.
"What the president needs to do is reach out not just to Republicans but to Democrats and to ensure that he gives them the political cover to do frankly what most of them know needs to be done," Portman said.
One of the GOP senators who dined with Obama last week said the president showed that he understood the scope of the problem, with Medicare paying out $3 in benefits for every $1 put in.
"I think he gets it," Sen. Tom Coburn of Oklahoma told NBC on Sunday. "And I think he`s genuinely reaching out. But you`ve got a lot of scabs and sores on people that it`s going to take a while for that to heal."
Another entitlement reform Obama has proposed would tighten the adjustment for inflation of benefits such as Social Security, meaning annual increases for future recipients would grow at a slower pace.
Opponents of the reform, known as "chained CPI" in reference to the consumer price index it involves, argue it hurts vulnerable senior citizens and others who most need their benefits.
If achieved, a grand bargain would give Obama a major political victory and a boost in cementing his desired presidential legacy after the controversial health care and Wall Street reforms of his first term.
Republicans also would get credit from moderates and independents for a willingness to compromise, but conservatives could punish them with primary challenges in 2014 and beyond.
After the repeated failure of previous efforts for a broad deficit reduction deal, attention has focused on a more limited agreement that would include some elements under discussion.
For example, a smaller agreement might end some tax breaks and loopholes while cutting Medicare costs paid providers, not beneficiaries, to achieve $500 billion or so in deficit reduction over 10 years.
Such an outcome, coupled with previous spending cuts and the January fiscal-cliff deal, would fail to reach the total $4 trillion in deficit reduction over the next decade that economists and political leaders have targeted as the minimum amount needed.
It also would allow both parties to simultaneously claim credit for making some progress after the past years of dysfunction while continuing to blame the other for preventing more.
The status quo outcome would mean continued brinksmanship over each pending fiscal deadline, as well as further economic uncertainty that already has lowered the U.S. credit rating and slowed growth.
For now, political leaders sound optimistic that resolve to move forward exists on both sides.
"I think there are things that we can do that don't offend either party's philosophy, that doesn't require someone to surrender their principles to make a good down payment on getting this debt and deficit under control," Ryan said Sunday.
His budget proposal will include provisions certain to be rejected by Democrats, such as eliminating 2010 health care reforms that comprise Obama's signature legislative achievement, as well as shifting Medicaid to a grant program for states and changing Medicare from a direct benefit to a direct subsidy program.
"We think that's the best way to make these programs work better, but are there things you can do short of that, that gets you closer to balancing the budget, that delays the debt crisis from hitting this country?" Ryan asked. "Yes, I think there are."
Obama's Medicare plan focuses mainly on reducing payments to drug companies and hospitals, though he would also raise revenue by asking wealthy seniors and new beneficiaries to pay more.
Democratic Sen. Tim Kaine of Virginia, a former governor who joined the chamber this year, told NBC that returning to a normal budgeting process creates a framework for debate and compromise.
"You`re going to start to see both (chambers) put out their budgets, laying out visions for how to keep the economy strong and also deal with the deficit," Kaine said, adding: "At the end of the day, we`re going to have to find a balanced solution and it will involve all elements. It will involve talking about revenues, talking about expenses, talking about entitlements. We have to do that."
CNNMoney's Tami Luhby and CNN's Kevin Liptak and Gregory Wallace contributed to this report.