WASHINGTON — The hard-fought bargain that narrowly thwarted a government shutdown sets the stage for far more consequential spending battles ahead between emboldened House Republicans and President Barack Obama and the Democratic-controlled Senate.

After arriving late Friday at a budget deal to cut $38 billion from current spending levels and fund the government for the remainder of the fiscal year, Republicans and Democrats claimed victory. Both sides quickly attempted to seize the momentum heading into looming fights over increasing the federal government’s ability to borrow money and a 2012 Republican budget proposal to tackle the long-range deficit by fundamentally overhauling Medicare and Medicaid.

The clashes to come this spring will determine whether the U.S. government goes into default and promise to shape, if not define, the political landscape going into the 2012 presidential election.

The upcoming spending votes could usher in wide-ranging policy changes affecting health care, social issues, environmental regulation and taxes.

The opening salvo could come this week with a planned vote in the House on the GOP’s budget blueprint for 2012. The plan, introduced last week by Budget Committee Chairman Paul Ryan, R-Wis., would reduce spending by $6 trillion over the next decade, in part by introducing profound reductions to popular government entitlement programs.

When both chambers return from a two-week recess May 2, debate will begin over raising the $14.25 trillion federal debt ceiling. The government’s debt is projected to pass that mark by mid-May, and although Treasury Secretary Timothy Geithner has said he could buy more time with emergency measures, Congress must act to raise the limit by July 8 or else the government would begin defaulting on its debt.

That, economists have warned, would send interest rates soaring and start another financial crisis.

Last week’s drama over whether Congress could reach a budget deal and prevent a government shutdown tested the resolve of both parties. Crisis was averted literally at the eleventh hour — just before 11 p.m. Friday, an hour before government agencies were to run out of money.

On Saturday, Obama signed into law a stopgap measure to keep the government funded until Congress officially passes the longer-term deal this week. And with the sense of crisis lifted from Washington, the president bounded up the steps of the Lincoln Memorial to celebrate before a cheering crowd of tourists.

“Because Congress was able to settle its differences, that’s why this place is open today and everybody’s able to enjoy their visit,” Obama said in his stop.

But the moment underscored how a divided government, its leaders tugged by divergent political constituencies, could easily be broken.

“It’s showed that neither side is afraid to have a really hardballed negotiation, that closing down the government is an option on other things and that neither side is afraid to take it to the edge of the cliff,” said Rep. Jack Kingston, R-Ga., who served during the 1995 shutdown.

The debt ceiling debate, which Sen. Kay Bailey Hutchison (R-Tex.) calls “Armageddon,” already has Wall Street and the business community anxious.

“The fact that we got up to the eleventh hour (in the budget debate) caused disruption and anxiety in a lot of people’s lives, but the difference of going down this same path with the debt ceiling, you don’t need to get to the eleventh hour before the markets start reacting,” Sen. Mark Warner, D-Va., said.

Leaders in both parties view this as must-pass legislation. The White House is urging passage of a debt limit increase with no amendments, but officials acknowledge privately that they may need to make concessions, perhaps in the form of substantial spending cuts, to win support from House Republicans.

“We’re here mopping up their spilled milk, to be honest,” freshman Rep. Michael Grimm, R-N.Y., said. “We’re in a financial crisis. If we don’t have massive cuts, we will lose the American dream for future generations.”

Many Republican freshmen have said they oppose increasing the debt limit, presenting House Speaker John Boehner, R-Ohio, with an immediate challenge.

House Republican leaders are considering attaching the Ryan budget to the debt ceiling bill as an incentive to win over tea party Republicans, according to leadership aides.

But the Ryan budget would be a non-starter in the Senate, where Democrats consider its proposed spending cuts and changes to Medicare and Medicaid to be far too extreme.

Under, the Ryan plan, seniors would pick from a list of private Medicare insurance plans and the federal government would only subsidize their coverage. Medicaid, the health program for the poor, would be turned into a block grants program, with the federal government letting states spend money as they see fit.

The Ryan budget does not address Social Security or tax loopholes for corporations, both potential areas of savings. And it would lower the top income and corporate tax rate to 25 percent.

In the Senate, Minority Leader Mitch McConnell of Kentucky outlined his strategy recently in a private session with Senate Republicans: He would make Majority Leader Harry Reid of Nevada rely only on Democratic votes to pass the bill, forcing vulnerable Democrats up for re-election in 2012 to vote for the measure to reach a 51-vote threshold, according to aides with knowledge of the talks. McConnell has also urged his caucus not to filibuster the debt ceiling, arguing that he does not want the party to be blamed for a debt crisis.

Democrats, meanwhile, plan to push for savings in two areas that were ruled off the table in the most recent budget fight: military spending and tax increases.

“We’re going to have to have an expanded playing field,” said Sen. Charles Schumer of New York, the No. 3 Senate Democrat. He also suggested that eliminating subsidies to oil companies would be another ripe target.

But some prominent voices in the party’s liberal base argued that Democrats will be at a disadvantage in these fights: By allowing Boehner to secure $38 billion in spending reductions last week – far steeper cuts than Democrats initially had been willing to concede – they have emboldened House Republicans, particularly those allied with the tea party, to seek more concessions next time when the stakes are higher.

“The tea partyers held the House Republicans hostage, and the House Republicans held the rest of the government hostage,” said Robert Reich, labor secretary under President Bill Clinton. “We can expect a repeat performance. Once you pay off hostage takers, there’s no end to how many times they’re going to demand more and more ransom.”