The Democratic-controlled Senate has signaled that it will not consider anything approaching the scale of cuts approved by the House, setting up a standoff that each side has warned could lead to a shutdown of the federal government early next month.

Saturday’s predawn vote was also the opening salvo in what is likely to be a long, bitter clash of philosophical ideas about fiscal policy on Capitol Hill, in statehouses around the country and in the 2012 presidential campaign, as Republicans repudiate the Keynesian strategies the Obama administration has relied on to navigate through the worst economic downturn since the Great Depression.

Republicans seemed to grow more excited as the final vote neared shortly after 4:30 a.m. “We have a mandate from the American people to cut spending,” declared Representative Judy Biggert of Illinois.

Treasury Secretary Timothy F. Geithner quickly criticized the House package, saying it would “undermine and damage our capacity to create jobs and expand the economy” at a time when unemployment remains high. Mr. Geithner, in Paris for a Group of 20 meeting of the world’s largest economies, said the administration was “confident that the Democrats and Republicans are going to come together on a program not just to reduce spending, but to reduce our long-term deficits.”

The White House had threatened to veto the bill even before it was approved.

In Washington, the fight in the weeks ahead will focus on paying for government operations through the end of the fiscal year on Sept. 30, and the need within the next few months to raise the federal debt ceiling. But the push by Republicans for spending cuts and new austerity is already shaking state capitals, including Madison, Wis., and Columbus, Ohio, where labor unions have begun protesting efforts to reduce benefits and weaken their collective bargaining rights.