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In one of Thursday’s other votes, senators rejected Mr. Ryan’s House-passed budget by a 59-40 vote, but in another, they voted to repeal a sales tax on medical devices that is part of President Obama’s health-care law. That vote was overwhelming and bipartisan, passing by a 79-20 margin.

Mrs. Murray’s budget calls for spending $3.7 trillion in fiscal 2014, and calls for taxes of about $3 trillion, leaving a deficit of nearly $700 billion. Over the next decade, her budget would spend $46.4 trillion and take in just $41.2 trillion in taxes, for accumulated deficits of more than $5 trillion.

By contrast, House Republicans’ budget, which passed that chamber on Thursday, would spend $3.5 trillion next year and $41.5 trillion over the next decade, compared with tax revenues of $3 trillion in 2014 and $40.2 trillion over 10 years.

The Republican plan would leave a half-trillion-dollar deficit next year, and accumulated deficits of $1.2 trillion over the decade — or about $4 trillion less than Mrs. Murray’s plan.

“We can’t continue to spend money that we don’t have. It’s as simple as that,” said House Speaker John A. Boehner, Ohio Republican, who warned of a looming “debt crisis.”

But Democrats said the budget ignored Mr. Obama’s 2012 victory, which they said showed voters back tax increases rather than spending cuts.

“We should instead be focusing on job growth and putting people back to work,” said Rep. Chris Van Hollen, Maryland Democrat.

The 221-207 House vote saw 10 Republicans join Democrats in opposition — the same number of defections as on Mr. Ryan’s budget last year, which became fodder for Democratic political attacks on the campaign trail.

Budgets are not signed into law, but provide a blueprint for both the tax and spending committees to move forward with bills this year. The renewed interest in passing budgets comes after Republicans wrote a law earlier this year that would withhold lawmakers’ pay beginning April 15 unless their chamber approved a blueprint.