WASHINGTON — However the debt limit showdown ends, one thing is clear: under pressure from Congressional Republicans, President Obama has moved rightward on budget policy, deepening a rift within his party heading into the next election.

Entering a campaign that is shaping up as an epic clash over the parties’ divergent views on the size and role of the federal government, Republicans have changed the terms of the national debate. Mr. Obama, seeking to appeal to the broad swath of independent voters, has adopted the Republicans’ language and in some cases their policies, while signaling a willingness to break with liberals on some issues.

That has some progressive members of Congress and liberal groups arguing that by not fighting for more stimulus spending, Mr. Obama could be left with an economy still producing so few jobs by Election Day that his re-election could be threatened. Besides turning off independents, Mr. Obama risks alienating Democratic voters already disappointed by his escalation of the war in Afghanistan and his failure to close the Guantánamo Bay prison, end the Bush-era tax cuts and enact a government-run health insurance system.

“The activist liberal base will support Obama because they’re terrified of the right wing,” said Robert L. Borosage, co-director of the liberal group Campaign for America’s Future.