In his first two years, President Obama pursued an agenda that dramatically increased government spending and ushered in the biggest change in social welfare policy since the Great Society. When he spoke to the country late Friday night, he sounded like a born-again budget cutter.

Americans may ask which is the real Obama, the politician who embraced the biggest stimulus package in the nation’s history, a bailout of the banks and a takeover of the automobile industry, or the one who on Friday hailed the new budget deal as including “the largest annual spending cut in our history.”

Nervous Democrats fear that Obama gave away too much in the last-minute agreement that averted a government shutdown. They worry even more about the coming fights over raising the debt ceiling and particularly Obama’s response to the budgetary blueprint outlined last week by House Budget Committee Chairman Paul D. Ryan (R-Wis.).

That response will come soon, perhaps as early as this week. White House officials see the debate over Ryan’s budget plan, which calls for deep cuts in Medicare and Medicaid, as far different from the one that ended Friday night.

That was a skirmish to survive, a debate over how much discretionary domestic spending should and could be cut for the rest of the fiscal year. The battle was fought on turf far more hospitable to Republicans, given the country’s concerns about spending that contributed to the Democrats losing the House in November.

The coming battle, which will be about fiscal priorities and society’s values as much as it is about controlling government spending, will be waged on ground that Obama’s advisers think is far better for the president and the Democrats.

“Paul Ryan laid out the congressional Republican vision of how you deal with deficits,” White House communications director Dan Pfeiffer said Saturday. “It is a vision starkly different from the president’s and particularly because of the lack of balance in his approach.”

Still, there are questions about how Obama will take on this battle. Will he be willing to draw bright lines in this debate? Or, will his instinct for compromise cause him to give away more than his Democratic supporters want.

In the negotiations that ended late Friday, Obama remained largely above the fray. The course he was hoping to steer was evident from his remarks shortly after the agreement was announced.

Most important was showing the country that he could make Washington work. “Like any worthwhile agreement, both sides had to make tough decisions and give ground on issues that were important to them,” he said.

At the same time, knowing that the public also favors reduced spending, Obama pointed to the size of the cuts in the new agreement while noting that his priorities had been preserved. The budget, he said, would “invest in our future.” He also put down a marker against the opposition by noting that he and the Democrats had fought to prevent the GOP from using the budget fight to advance a social-issue agenda.

Democratic pollster Peter Hart said the outcome of the budget fight strengthens Obama politically. The president showed he could reduce spending — what Hart called a political crown jewel — while protecting the rights of family planning, decisions highly popular with the public.

“From this fight,” Hart said in an e-mail, “he protects his liberal flank while positioning himself as a moderate on fiscal issues. In an era where voters want compromise, the president looks like a tough negotiator rather than a weak compromiser or an ideological purist.”

Still, the cuts Obama and Senate Majority Leader Harry M. Reid (D-Nev.) agreed to in order to win the support of House Speaker John A, Boehner (R-Ohio) disturbed many Democrats. They fear that Boehner will be emboldened by the outcome to take an even harder line in coming fights and that Obama will yield even more ground.

A labor Democrat said Saturday that he thinks the president has some latitude with the progressive wing of the party, given the policies of the opposition. “There will be some unease and restlessness, but I’m not hearing a lot of people saying they’re ready to abandon ship,” said this Democrat, who requested anonymity to speak candidly. “In general, there’s kind of a resignation of this is the guy and . . . priority number one is getting him reelected in 2012.”

But Bob Borosage of the progressive group Campaign for America’s Future said that the more Democrats learn about the specific cuts enacted in the current budget deal, the more alarmed they will be — and the more the pressure will increase on Obama to lead the fight against Ryan’s blueprint.

“No one is going to have patience for the strategy that Reid played,” he said. “They will expect the president to come out right away and expose how preposterous Ryan’s plan is. It’s bald and brazen and incredibly indefensible, and the president better make that clear.”

Obama advisers reject any suggestion that the president has changed course or philosophy since the midterm shellacking. “It would be revisionist history to view this as a change in philosophy,” Pfeiffer said. “It’s really a change in the state of the economy. That means the actions we took in the first two years, and particularly at the beginning of the administration, are not necessary right now.”

Obama advisers also suggest that the president’s goal in challenging Ryan’s priorities is not simply to score political points. They say Obama hopes that a vigorous debate over how to reform entitlements and lasso government spending will lead to an eventual bipartisan agreement.

To this point, however, the president has offered little more than generalized exhortations about the need to deal with the long-term problem of debt and deficits. To his credit, Ryan has gone much further, as did the president’s own debt and deficit commission.

Obama’s willingness to engage directly, and to lay out a more detailed vision, will begin to show us how much he is prepared to risk to get to that goal.

Staff writer Peter Wallsten contributed to this report.