Sen. John McCain, R-Ariz., told CNBC on Thursday that lawmakers should try the regular budget process for a change.
"We all know that Republicans were punished the most by this," McCain admitted. But Democrats were, too, and so was the president, he added. "There's reasons for them not wanting to do this again as well."
"I'm assuming that [a Grand Bargain] probably won't happen because it's been tried so many times with all the different gimmicks: Select Committee, Super Committee, Gang of ... 'insert your number,'" the Arizona Republican said in a "Squawk Box" interview.
"Why don't we try the regular process. The House passes a budget. The Senate passes a budget. Then they confer. Then they come out with a budget," he said.
Sen. Bob Corker, R-Tenn. agreed in a separate interview on "Squawk Box" that a grand bargain was likely.
"For what it's worth, I don't think there's going to be a 'big deal' in January,' Corker said. "I think what we need to begin to do is look at mandatory reforms and look at those relative to the discretionary cuts that we have in the Budget Control Act."
(Read more: Just 'locker room talk' in DC: Sen. Corker)
The compromise deal signed by President Barack Obama early Thursday extended the debt ceiling until Feb. 7 and reopened the government by approving funding until Jan. 15.
McCain said Obama seems willing to work with the GOP. "This president, like all presidents that have had a second term, look at their legacy," he said. "Part of that has been, he has had an outreach" to Republicans.
In an earlier "Squawk" interview, Grover Norquist, founder of Americans for Tax Reform, said that Republicans want to look at closing loopholes as part of broad tax reform, but won't accept anything that's not revenue neutral.
(Read more: No new taxes, cut entitlements: Norquist)
But Rep. Chris Van Hollen, D-Md., told CNBC: "You don't begin a negotiation by saying you refuse to talk about certain things. If they are going to take that position, it's going to be hard to move forward." Van Hollen is the top Democrat on the Budget Committee whose chairman, Paul Ryan, will be leading Republicans in debt and spending negotiations going forward.
"Everybody who comes to the negotiating table should agree that they're not going to use the club of the threat of government shutdown or default again to get their way," said Van Hollen, referring to failed effort by Republicans to try to use the debt ceiling and government funding as leverage to defund or delay Obamacare.
Sen. Heidi Heitkamp, D-N.D., told CNBC that "we've got a long road ahead" in fixing the budget. "How we got here is people drawing red lines—we're not going to do this unless I get what I want," she said. "Everything should be on the table," including entitlement programs and the current nominal tax rate.
McCain won't address whether he'd agree to any new revenue as part of budget negotiations—a condition that Democrats demand.
He said, however, that he'd support closing "some of these [tax] provisions that have been put in by special interests here in Washington," adding "we ought to repeal them rather than wait until 'tax reform,' which is some huge holy grail out there that we probably will never find."
"I was offended when we made some of those tax loopholes," McCain stressed, "and I'll be damn glad to close them."