WASHINGTON — Senate Democrats and House Republicans on Tuesday outlined vastly divergent approaches to shoring up the government’s finances, a reminder of how far apart they remain on fiscal policy even as both sides insist publicly that a bipartisan compromise is possible.

As part of the effort to find common ground, President Obama made a rare appearance at a gathering of Democratic senators — his first of four meetings with lawmakers on Capitol Hill this week — to explore ways that the two parties could overcome differences that have deadlocked the budget process for much of the last five years.

But in many ways, the two parties seemed to be working in parallel universes.

House Republicans, led by Representative Paul D. Ryan of Wisconsin, presented a tax and spending plan that relies on many of the same policies that became lightning rods for critics during the 2012 presidential campaign, when Mr. Ryan was the party’s vice-presidential nominee. At the White House, a senior administration official said that the Republican budget demonstrated how complicated negotiations would be.

The Republican plan sets out to balance the budget in a decade and would cut spending by $4.6 trillion through 2023, in large part by rolling back many of Mr. Obama’s signature legislative accomplishments. It would repeal the health care overhaul of 2009, eliminate the subsidized insurance exchanges and Medicaid expansion that make up the core of the law, and turn Medicare into a system of private insurance plans financed by federal vouchers.