WASHINGTON  President Obama conceded on Tuesday that his new budget does not do enough to resolve the nation’s long-term fiscal problems, but he counseled patience, suggesting that he would eventually come together with Republicans on a broad deal.

But, Mr. Obama said at a news conference, any such compromise to address Medicare, Medicaid, Social Security and the tax system is months away and will first require an effort to build bipartisan trust  even as Democrats and Republicans battle intensely over how much to cut from the current year’s domestic spending.

The president spoke as Republicans on Capitol Hill accused him of a lack of leadership for not proposing a bolder budget for the fiscal year that starts Oct. 1. Yet behind the scenes are signs that both parties, for all their public crossfire, are reassessing the politics of deficits.

The debt crises last year in Greece and other European countries served as a warning about the economic perils of chronic budget imbalances, and the rise of the Tea Party movement reflected a broader concern among Americans about the nation’s rapidly mounting debt.