But House Democrats easily defeated Republican alternatives and won backing for their budget from all segments of their party, from conservative Blue Dogs to urban liberals. The 233-to-196 vote, though hardly overwhelming, actually reflected a strong show of Democratic support for the budget, since it often barely passes. It was the first time in a dozen years that a budget had received more than 230 votes. Twenty House Democrats opposed the budget; two Senate Democrats did.

Image Speaker Nancy Pelosi and other House Democratic leaders before passage of a $3.6 trillion budget for the 2010 fiscal year. Credit... Doug Mills/The New York Times

The chief Republican alternative, officially supported by the party leadership, was defeated 293 to 137, with 38 Republicans opposing it.

The total lack of Republican backing for the Democratic plans was reminiscent of the House vote this year on the $787 billion economic stimulus program. But the budget’s approval was nonetheless viewed as a victory for the new White House, particularly because most moderate and conservative Democrats went along with the president’s push for more spending.

In the Senate, where lawmakers engaged in their annual “vote-a-rama,” discarding or approving piles of amendments, Democrats easily defeated an alternative offered by Senator John McCain of Arizona and a handful of fellow Republicans that would have essentially frozen federal spending except for the military.

“We are just going on as if it were business as usual,” said Mr. McCain, asserting that no family in America was increasing spending, while the federal government was. “We can,” he said, “because we print money.”

Among the amendments that won Senate approval was a bipartisan proposal that would raise the estate tax exemption by $1.5 million, to a total of $5 million, and reduce the tax’s maximum rate by 10 percentage points, to 35 percent.

Both the House and Senate budgets pared spending from the president’s initial request and made other adjustments intended to reduce the annual deficit to less than $600 billion within five years, about half the $1.2 trillion projected for the 2010 fiscal year, which begins Oct. 1.