On NBC's "Meet the Press," Rep. Paul Ryan, R-Wis., chairman of the House Budget Committee, said: "I feel like we had a pretty good outcome. We represented one-third of the negotiators, but we got two-thirds of the spending cuts we were asking for."
But he added, "This is really still a drop in the bucket. We want to move from talking about saving billions of dollars to going on to saving trillions of dollars."
On the coming debate over raising the federal debt ceiling, House Speaker John Boehner, R-Ohio, has said: "Mr. President, not a chance you're going to get a clean bill. ... There will not be an increase in the debt limit without something really, really big attached to it."
Ryan said, "Our strategy is not to default. Our strategy is to get spending under control."
On CBS' "Face the Nation," Sen. Charles Schumer, D-N.Y., claimed victory for the Democrats in Friday's 11th-hour compromise because "We don't cut the seed corn, the things like teachers and Head Start and cancer research and helping kids go to college."
On the same program, Sen. Jeff Sessions, R-Ala., said: "The American people are saying, children, you've misbehaved; you've spent too much of our money. And I think, through their elected representatives, they will insist that we make some changes in how we operate the budget.
"You could have a two-year budget, for example, instead of one. I think that would help. We can put statutory caps on spending. We can have a balanced budget constitutional amendment."
Schumer responded: "This is playing with fire. And I would urge both sides to take the threat of not renewing the debt ceiling off the table."
On "Fox News Sunday," House Majority Leader Eric Cantor, R-Va., saw a GOP gain.
"I have to believe that the president and the White House are beginning to sense the American people get it," he said. "You know, we have a fiscal train wreck before us."
He saw the debt debate as a "time leverage moment ... in which the White House and the president will actually capitulate to what the American people want right now. They don't want to raise taxes. They don't want spending to continue to spiral out of control."
The Senate's No. 2 Democrat, Richard Durbin of Illinois, said on CNN's "State of the Union" that his party succeeded in protecting "childhood education, Pell grants for kids from low-income families who want to go to college, medical research grants. … These are the things which were essential, and at the end of the day we won the battle."
White House political adviser David Plouffe, speaking on ABC's "This Week," said, "We protected medical research, community health centers, kids on Head Start. We were not going to sign off on a deal that cut those things."
Rep. Jeb Hensarling, R-Texas, echoed his GOP colleagues in saying,
"No, we do not want America to default on its debts, but the president is going to have to cut up the credit cards."
Rep. Mike Pence, R-Ind., had a somewhat different take: "It sounds like John Boehner got a good deal. Probably not good enough for me to support it, but a good deal nonetheless."
Rep. Chris Van Hollen, D-Md., said: "It will be hugely dangerous for the Republican colleagues to play a game of chicken on the debt ceiling. You would see an economic catastrophe if the United States defaulted on its debt."