WASHINGTON — Many Republican conservatives — notably some elected for the first time last year — have grown increasingly frustrated over plans to keep the government running for another three weeks, saying they want longer-term, more serious spending cuts.

The House of Representatives, where Republicans have a 241-192 majority, plans to vote Tuesday on keeping the government funded through April 8. The package cuts spending by $6 billion.

While Republican leaders Monday were guardedly confident the bill will pass, they expect grumbling, an unpredictable number of Republican no votes and lots of warnings this is the last short-term extension most GOP lawmakers will accept.

“When I was elected last year, it was to change the culture in Washington. The status quo here is, ‘Take your time. We’ll get to it.’ We don’t have the time to wait around,” said freshman Rep. Tim Huelskamp, R-Kan., who plans to vote no.

“Cutting the size and scope of government won’t be possible as long as Congress squabbles over cutting millions of dollars when our nation is $14 trillion in debt,” added freshman Rep. Jeff Duncan, R-S.C., another anticipated no vote.

If the House approves the extension, the measure would then go to the Democratic-dominated Senate, which would be expected to concur, and then to President Obama. Vice President Joe Biden and congressional leaders are trying to negotiate a deal to keep the government running through Sept. 30, the end of fiscal 2011.

Current spending authority expires Friday; if no further funds were provided, much of the government would shut down.

Republicans want a budget-cutting plan that slices $61 billion from current year spending, but Democrats have blocked it. Congress approved a two-week stopgap earlier this month that cut $4 billion.

Six Republicans voted against that measure. But this time, said many conservatives, they’ve had enough of the piecemeal solutions, and could vote no.

“With the federal government facing record deficits and a mammoth debt hanging over our economy and our future, we must do more than cut spending in bite-sized pieces,” said Rep. Jim Jordan, R-Ohio, chairman of the Republican Study Committee, the leading House Republican conservative group, who opposes the latest proposal.

The key to the bill’s fate Tuesday appears to lie with the House’s 87 Republican freshmen, many of whom were elected last year with the backing of the tea party movement.

Some tea party leaders have made it clear they’re impatient with Congress’ slow progress on spending. “Where are the calls for the cutting of hundreds of billions?” asked Tea Party Nation founder Judson Phillips recently. “They certainly are not coming from (House Speaker John) Boehner.” As a result, Phillips said, “The tea party movement should find a candidate to run against John Boehner in 2012.”