WASHINGTON — President Obama made the case Wednesday for slowing the rapid growth of the national debt while retaining core Democratic values, proposing a mix of long-term spending cuts, tax increases and changes to social welfare programs as his opening position in a fierce partisan budget battle over the nation’s fiscal challenges.

After spending months on the sidelines as Republicans laid out their plans, Mr. Obama jumped in to present an alternative and a philosophical rebuttal to the conservative approach that will reach the House floor on Friday. Republican leaders were working Wednesday to round up votes for that measure and one to finance the government for the rest of the fiscal year.

Mr. Obama said his proposal would cut federal budget deficits by a cumulative $4 trillion over 12 years, compared with a deficit reduction of $4.4 trillion over 10 years in the Republican plan. But the president said he would use starkly different means, rejecting the fundamental changes to Medicare and Medicaid proposed by Republicans and relying in part on tax increases on affluent Americans.

The president framed his proposal as a balanced alternative to the Republican plan, setting the stage for a debate that will consume Washington in coming weeks, as the administration faces off with Congress over raising the national debt ceiling, and into next year, as the president runs for re-election.