(CNN) -- President Barack Obama wrapped up a three-day bus tour of Iowa on Wednesday by accusing Mitt Romney of dishonest attacks on his record, while the certain Republican nominee continued to call Obama's re-election effort a hateful divide-and-conquer strategy.
With less than three months until the November election, the negative campaign has become even more bitter since Romney chose House Budget Committee Chairman Paul Ryan as his running mate.
Ryan is best known for a conservative budget plan passed by the Republican-led House that would partially privatize Medicare, which Democrats say would kill the government-run health care program for senior citizens.
A contentious struggle between the Obama and Romney camps to favorably frame the sensitive issue of Medicare has escalated campaign rhetoric to a personal level rarely reached in a presidential race.
Romney continued the negative tone on Wednesday, saying in an interview with CBS that the Obama campaign is "about division and attack and hatred" that is "designed to bring a sense of enmity and jealously and anger."
"The president seems to be running to hang on to power," the former Massachusetts governor said. "I think he'll do anything in his power to try and get re-elected."
Obama used his first campaign speech of the day to challenge Romney over a new television ad that accuses the president of cutting more than $700 billion from Medicare as part of the 2010 health care reform law.
"I think they know their plan is not very popular. You can tell that because they are being pretty dishonest about my plan," Obama said of his Republican rivals. "Especially, by the way, when it comes to Medicare. This is something I have got to point out here because they are just throwing everything at the wall to see if it sticks."
Raising his voice, Obama insisted that his health care policies strengthened Medicare, including reforms that saved senior citizens money on their prescription drugs and aimed to eliminate waste without cutting benefits.
The Ryan plan would shift Medicare costs to beneficiaries by implementing a voucher system for helping them buy increasingly expensive private insurance, Obama said.
"My plan has already extended Medicare by nearly a decade," he said. "Their plan ends Medicare as we know it."
Ryan said said the president had raided Medicare and the White House was calling it an achievement. Republicans welcomed a discussion on the issue, he said.
"We need this debate and we will win this debate," he told an audience at his alma mater, Miami University in Oxford, Ohio.
In Virginia on Wednesday, Vice President Joe Biden sounded Democratic attack lines against Romney, depicting him as an out-of-touch multimillionaire intent on reviving policies that benefit the wealthy at the expense of the middle class.
Recalling a saying by his own father -- "Don't tell me what you value; show me your budget and I will tell you what you value" -- Biden listed Romney policy proposals that he said demonstrated the values of the Republican challenger.
These, Biden said, included repealing health care and Wall Street reform legislation, cutting spending on education, and reducing the size and scope of entitlements like Medicare, Medicaid and Social Security.
"These guys aren't hiding the ball," Biden said, employing a football metaphor. "... We know exactly what they want to do."
On Tuesday, Romney and Republicans bristled when Biden accused Romney of promising to lift regulations on big banks in an effort to "unchain Wall Street," adding: "He is going to put y'all back in chains."
Former Virginia Gov. Doug Wilder, a Democrat and the first African-American to be elected governor of Virginia, criticized Biden on Wednesday's "The Situation Room with Wolf Blitzer"and said the remarks were "appeals to race."
Biden explained that he was playing off Republican references to the "shackles" that regulations place on the private sector, but Romney said Wednesday the comment was beneath the dignity of a presidential campaign.
At the same time, Romney sounded conciliatory by adding that "no one is talking about deregulating Wall Street."
"Of course, we have to have regulation on Wall Street and on every street to make sure our county works well," said Romney, who has previously called for repealing the Wall Street reform law that responded to the 2008 financial crisis.
Romney has yet to detail what regulations he would support to replace that measure.
Overall, the campaign focus has remained on Ryan and his budget plan. It calls for sharp cuts in non-military spending to shrink government as well as stark reforms to Medicare and the Medicaid program, which provides health care to the poor and the disabled.
Ryan's proposals include the provision that Medicare-approved private insurers would one day compete with traditional government-sponsored Medicare on an exchange. The intention of his plan is to remake Medicare so that it remains financially viable for future generations, while preserving the benefits of current seniors and those who will qualify in the next 10 years, Ryan told CBS on Sunday.
Republicans reject the Democratic tactic to tie Romney to the Ryan proposal, saying he has his own budget and tax plans that are similar to Ryan's but include key differences.
Last month, the Congressional Budget Office said repealing the health care reform law, as called for by Romney and Ryan, would increase spending on Medicare by $716 billion through 2022.
The non-partisan agency that reviews congressional budgets also said keeping Obama's health care reforms in place would not mean a $716 billion decrease in Medicare spending, as claimed by Romney and his campaign ad.
The Obama campaign called Romney's claim "dishonest and "hypocritical."
"The savings his ad attacks do not cut a single guaranteed Medicare benefit, and Mitt Romney embraced the very same savings when he promised he'd sign Paul Ryan's budget," Obama campaign spokeswoman Lis Smith said Tuesday.
Romney sounded undaunted Wednesday, repeating the claim in the CBS interview when asked to comment about how Ryan's plan and Obama's health care reforms both include the $716 billion in Medicare savings that he criticizes.
"Congressman Ryan has joined my campaign, and his campaign is my campaign now. We're on exactly the same page," Romney said. "My campaign has made it very clear. The president's cuts of $716 billion to Medicare, those cuts are going to be restored if I become president and Paul Ryan becomes vice president."
Ryan has yet to comment on the difference between his Medicare proposal, which was part of a broader budget and tax plan passed by House Republicans.
A new poll released Wednesday showed little impact so far from Romney's choice of Ryan as his running mate, which was announced on Saturday.
The Gallup Daily Tracking Poll showed Romney holding a statistically insignificant 47%-45% edge over Obama in the four days since the announcement, compared to 46%-45% in the four days prior to it.
First lady Michelle Obama joined the president for his Iowa events Wednesday, which concluded a three-day bus tour through the state where Obama's 2008 campaign first took off. It was the first time the couple appeared together on the campaign trail since the first events of the re-election effort in May.
CNN's Ashley Killough, Rachel Streitfeld, Gregory Wallace, Paul Steinhauser and Peter Hamby contributed to this report.