House Minority Whip Steny Hoyer (D-Md.) told CBS that the new approach offers a way forward, but called it a "missed opportunity." He said while he is glad the plan will avoid default, he wishes Congress had been able to agree on a larger deal that included revenue increases.
Hoyer said he is fed up with the behavior in Washington, and that he lacks confidence the difficulties of this debate will change the way deals are reached in the future. Hoyer said House members will need more time to review the plan before he can confirm whether he thinks it will pass.
"Debt default is not an option. We all understand that, but the sad news is we're so late getting to an agreement."
Sen. John McCain (R-Ariz.) spoke with "Imus in the Morning" Monday on Fox Business, saying it is "very important" an agreement be reached and it is "very likely" the new deal will be passed.
McCain said while there are things not to like in the bill, it moves in the right direction of spending control. He raised concerns that the plan would cut too much from defense spending.
The senator addressed his earlier Hobbit comments by saying it was unrealistic to tell the American people a balanced-budget amendment could pass in the Senate as it is currently constituted.
"At least in this deal you are cutting the budget more than you are increasing the debt limit … at least we have resolved an impasse for a period of time."
Sen. Bob Corker (R-Tenn.) told CNBC Monday morning he believes the new plan will pass in the House and Senate, but that he will need to spend more time looking at the bill before making a final decision.
While he doesn't believe this bill will make much of a dent in the debt, he said, he was glad it got people thinking about the issue. He called debt the "issue of the decade."
"This is no grand bargain, this is no seminal moment. Candidly I have a feeling it's not much of anything, but at least debt was the center of this discussion."
Rep. Connie Mack (R-Fla.) told MSNBC's "Morning Joe" he will vote against the new debt deal because he can't vote for a deal that increases the deficit without a solution to cut spending.
He said despite his objections to the proposal, he thinks it will pass in the House.
He praised the Speaker for getting the votes he needs to pass a bill.
"I haven't heard anything over the past couple of weeks that I could support."
Rep. David Schweikert (R-Ariz.) said he has concerns over potential tax increases and future cuts in the bill. Schweikert said, while he is undecided, he thinks Boehner will have a majority of Republicans to pass the bill in the House, as well as potential votes from Democrats.
However, he told Bloomberg he doesn't believe the new deal is substantial enough to prevent an eventual debt downgrade from the ratings agencies.
"I'm trying to reserve my judgment until I read the very last page, but there are parts of it that are a bit troubling."