(CNN) -- As the Pentagon launched a barrage of airstrikes into Syria late Monday, Sen. Tim Kaine, D-Virginia, who was an early backer of President Obama's first presidential campaign and his hand-picked chairman to run the Democratic National Committee, says he is concerned about presidential military action into Syria without congressional authorization.
"The point I think is so critical is the President shouldn't be doing this without Congress and ... Congress shouldn't be allowing it to happen without Congress," Kaine said Tuesday at a form at the liberal leaning Center for American Progress.
Kaine, however, said he is supportive of ongoing talks between the administration and congressional leadership on a possible new congressional war authorization.
The House and Senate left town last week so that members could go home to campaign for the midterm elections. Before Congress left, both chambers voted on a narrow measure that gave Obama the authority to train and arm Syrian rebel groups.
Congress did not act on a more broad measure that would have given the President the authority to expand its effort against ISIS in Iraq and Syria. While Obama said he would welcome congressional authorization, Republicans and Democrats were split on whether he had authority from existing authorization focused on al Qaeda. Some thought that the President needed additional congressional approval.
Most members of Congress expected the airstrikes to occur after they returned home to their districts, and privately, many of them conceded that they were relieved not to have to vote on a controversial topic just weeks before voters were to go to the polls in November.
House and Senate leaders said they were open to voting on a new measure giving new parameters for military action against ISIS, but not until after the election.
Criticism of the air strikes is bipartisan, ranging from concern over mission creep to waging war unilaterally.
Rep. Justin Amash, R-Michigan, a tea party favorite, ripped congressional leaders for skipping out on a debate on military action.
"It's irresponsible & immoral that instead of debating & voting on war, congressional leaders chose to recess Congress for nearly two months," he said in a tweet Monday night.
It's irresponsible & immoral that instead of debating & voting on war, congressional leaders chose to recess Congress for nearly two months.— Justin Amash (@repjustinamash) September 23, 2014
Anti-war Republican, Rep. Walter Jones of North Carolina, who like Kaine and Amash voted against arming the moderate Syrian rebels, said he was "disappointed" that the administration carried through with the airstrikes without congressional support. He co-authored a letter to House Speaker John Boehner urging a vote on war authorization.
"This reminds me of the Bush administration," he told CNN, referring to another expansion of military action. "I am not sure how much more we can ask of the military and the taxpayers without Congress having a debate."
While supportive of the strikes, Rep. Chris Van Hollen, a member of the Democratic House leadership, warned of mission creep, saying in a statement and in a tweet that the House should vote on a new war authorization that precludes any possibility of putting U.S. combat troops on the ground.
Obama's supporters are usually his detractors. Most of the positive reaction from lawmakers came from those who have been the most strident in their push for military action were the first to respond, and they did so enthusiastically.
On Monday, President Obama personally called House Speaker John Boehner, House Minority Leader Nancy Pelosi and Senate Majority Leader Harry Reid to notify them that the military operation inside Syria would begin in the evening.
Boehner said he supports the airstrikes, "understanding that this is just one step in what must be a larger effort to destroy and defeat this terrorist organization."
Democrats and Republicans who lead key committees approved of the President's move, including House Armed Services Committee Chairman Buck McKeon, who said "this is one step in what will be a long fight against ISIL," another acronym that refers to ISIS, or the Islamic State in Iraq and Syria.
Before the strikes, Vice President Joe Biden reached out to one of the administration's most vocal critics, Sen. Lindsey Graham, R-South Carolina, who told CNN's Dana Bash that Biden told him the airstrikes would be "intense" and a "sustained effort."
Graham said he told Biden he was "very supportive" of the administration's move and would do what was needed of him to corral Congress if further congressional authorization is needed.
ISIS has emerged as a campaign issue. Senate candidate Scott Brown, R-New Hampshire, released a television advertisement just after airstrikes in Syria commenced. While the ad didn't mention expanded military action into Syria, it tied his challenger, Democratic Sen. Jeanne Shaheen, to the President, who has low approval ratings in New Hampshire.
"Anyone who turns on the TV these days knows we face challenges to our way of life. Radical Islamic terrorists are threatening to cause the collapse of our country. President Obama and Sen. Shaheen seem confused about the nature of the threat. Not me," Brown says in the ad.
Shaheen, meanwhile, continues to insist that a hard line be taken against ISIS, saying she has "supported and will continue to support aggressive action to destroy ISIL."
CNN's Ted Barrett contributed to this report.