WASHINGTON  With President Obama’s release on Monday of a budget for next year and House action this week on a Republican plan for immediate deep spending cuts, the nation is getting its clearest view since the president took office of the parties’ competing visions of the role of government, the urgency of addressing the deficit and the best path to long-term economic success.

Mr. Obama used his budget for the fiscal year 2012 and beyond to make the case for selectively cutting spending while increasing resources in areas like education and clean energy initiatives that hold the potential for long-term payoffs in economic growth. With this year’s deficit projected to hit a record, $1.6 trillion, he laid out a path for bringing down annual deficits to more sustainable levels over the rest of the decade.

Republicans said it was not nearly enough to address chronic fiscal imbalances and reduce the role of the federal government in the economy and society.

Neither party has put forward specific proposals to begin grappling with the most pressing long-term budget problem: the huge costs in the Medicare, Medicaid and Social Security programs as the population ages and medical costs rise, a bill that could overwhelm the government and crimp the economy if not addressed.