As both sides sort out who won and who lost in the deal to keep the government running, the next phase of budget wrangling ensues.
The current-year budget deal struck Friday night still needs full congressional approval this week.
President Obama will deliver a speech Wednesday on the budget and the long-range deficits.
And sometime during the week, the House is expected to approve a new budget plan for next year that includes big changes in Medicare and Medicaid.
And none of that is to mention the looming battle about raising the federal debt ceiling.
The Current-Year Budget
Senior adviser David Plouffe announced Sunday that President Obama will address the nation Wednesday on the topic of reducing the deficit. On NBC's Meet the Press, Plouffe indicated that the president will embrace more of the recommendations from the bipartisan debt commission he appointed last year.
"Many of the debt commission's suggestions were in the president's budget," Plouffe said. "For instance, freezing the pay of federal workers for a period of time. Fundamental reform in the government. We obviously then have to do more, and that's what the president is going to lay out."
But for Republicans, the president is a late arrival to the effort to cut government spending.
Also on Meet the Press, House Budget Committee chairman Paul Ryan (R-WI) said the GOP leadership feels good about last week's deal, which includes $38 billion in cuts for the rest of the current fiscal year.
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 and saving trillions of dollars."
There have been loud complaints from liberal Democrats that last week's deal cut too much. And a lot of Republicans, especially those aligned with the Tea Party, say the GOP leadership got far too little — meaning the Republican leadership may have to rely on Democratic votes to get the deal finalized later this week.
2012: Ryan's New Budget Plan
Also on the docket for later in the week is a new budget resolution written by Rep. Ryan. Most controversial is its plan to turn Medicare for seniors into a subsidized insurance program and Medicaid for the poor into a block grant program run by the states.
"Medicaid is broken, and throwing more money at a broken system doesn't work," Ryan said. "We've gotten dozens of letters from governors saying, 'Give us the freedom to fix Medicaid our own way in our own states.' And we're giving them that freedom."
The Ryan proposal makes permanent the tax cuts from the Bush years for all income groups and lowers further the rate for the highest incomes. So Democrats see an opportunity to paint the GOP as cutting programs for the poor and the middle class while pursuing new tax breaks for the well-off.
"I don't think the American people are going to sign up for something that puts most of the burden on the middle class, people trying to go to college, on senior citizens, while not just asking nothing of the wealthy," Plouffe said.
The Debt Ceiling
Then there's the other looming showdown over the debt ceiling, which now stands at $14 trillion but will soon need to be increased so the nation can meet its outstanding obligations.
Sen. Dick Durbin (D-IL) is part of a bipartisan group of six senators working together on solutions to the long-term deficit question. On CNN Sunday, Durbin said it's dangerous to play politics with the debt ceiling.
"Now instead of risking government shutdown, we are risking a second recession. ... If we default on America's debt with this debt ceiling, it will have a dramatic negative impact on America's economy," he said.
But it's not so clear-cut for many Republicans, especially those elected with help from the Tea Party. Among them is Bill Huizenga of western Michigan, who was far from satisfied on NPR's Weekend Edition Saturday.
"I'm not sure what we're doing, you know," he said. "We had outpatient surgery last night. What we need is a heart transplant, and we have got to get more serious about this."
All of that shows the fight to find a compromise last week was just a preview of coming confrontations for this Congress and White House.