The House passed legislation on Tuesday to fund the government through Sept. 30 and avert a shutdown at the end of the week, in a party-line vote that reflected how Republican fiscal hawks have swallowed their concerns about spending in deference to President Trump.

The move sent the measure to the Senate, where Democrats are facing a political dilemma over whether to support it and hand Mr. Trump wide leeway to continue his assault on federal programs and workers, or oppose it and risk being blamed for a government shutdown.

The bill would keep last year’s spending levels largely flat, but would increase spending for the military by $6 billion. It would slightly decrease spending overall, because it would not include funds for any projects in lawmakers’ districts or states. And it would force a cut of more than $1 billion from the District of Columbia’s budget for the rest of the fiscal year.

The vote was 217 to 213, with only one Republican, Representative Thomas Massie of Kentucky, voting against the legislation. One Democrat, Representative Jared Golden of Maine, voted yes.

G.O.P. lawmakers supporting it and Democrats opposing it gave the same reason: They argued that the stopgap bill gave Mr. Trump latitude to continue his campaign to dismantle and defund major pieces of the federal government through Elon Musk’s Department of Government Efficiency, or DOGE.

In the Senate, Republicans would need the support of several Democrats to push the measure past a filibuster and allow it to pass and get to Mr. Trump’s desk before the March 14 midnight deadline to extend federal spending. Senate Democrats have widely criticized the measure, but some, especially those from swing states, have not ruled out ultimately voting for it.

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