WASHINGTON (AP) — Republicans won sweeping victories last November by taunting Democrats with "Where are the jobs?" Democrats are now throwing those taunts back, saying it's Republicans who will knock thousands of Americans out of work with their demands for deep cuts in federal spending.

The attacks have caught Republicans at an awkward moment, as they shift their chief emphasis from creating jobs to reducing the size of the government and its deficits. They are finding it hard to claim they can do both at the same time.

Republicans say a smaller government eventually will spur private-sector job growth. Many economists challenge that claim, noting that the government helps pays for research, infrastructure, education and other programs that provide both public- and private-sector jobs. GOP leaders already acknowledge that thousands of government workers would lose their jobs in the short run under the $61 billion cost-cutting bill House Republicans are pushing this week.

If that happens, "so be it," said House Speaker John Boehner, R-Ohio. "We're broke."

Boehner's allies say that it's impossible to trim federal spending without laying off government workers but that those workers eventually will recover. "They found their way into public jobs," said Rep. Tom Price, R-Ga. "They can find their way into private jobs" as the economy improves, he said.

Democrats and many mainstream economists, however, dispute GOP claims that deep federal spending cuts will lead directly to more private-sector jobs.

Boehner forwarded a letter to the White House from 150 economists — many with conservative backgrounds — saying: "To support real economic growth and support the creation of private-sector jobs, immediate action is needed to rein in federal spending." The three-paragraph letter did not seek to document a link between lower government spending and increased jobs, and some rival economists said it would be hard to do so.

With unemployment at 9 percent, the evidence that federal spending hurts job growth "is thin to nonexistent," said Princeton economist Alan Blinder. If the economy were running at full capacity, he said, Republicans would have a valid argument in saying that an extra federal hire or expenditure might displace a private-sector hire or expenditure. But there's a lot of "slack in the economy," he said.

Alexander J. Field, an economics professor at Santa Clara University, said he had "very little sympathy for the sentiments" in the letter Boehner forwarded. Spending cuts should be pursued when economies are strong, not weak, he said, and the House Republicans' agenda would probably increase unemployment.

Senate Democrats said Wednesday the House GOP plan would eliminate nearly $700 million in Title I grants to schools with disadvantaged students, and about "10,000 teachers and aides could lose their jobs." Congressional offices circulated White House budget office estimates saying the Republican bill would cut Head Start by more than $1 billion, leading to the layoffs of about 55,000 teachers and staff.

The liberal Economic Policy Institute says that overall, the House GOP plan "would likely result in job losses of just over 800,000."

The office of House Majority Leader Eric Cantor, R-Va., criticized the group's use of a "fiscal multiplier" in its analysis. John Irons, an economist and chief researcher for the Economic Policy Institute, said the multipliers are a standard, broadly accepted tool used by the Federal Reserve, Wall Street analysts and others.

Boehner spokesman Mike Steel said, "Our goal is to create the environment for private-sector job creation by ending Washington Democrats' spending binge — because their 'stimulus' has utterly failed to create the jobs they promised."

The Obama administration's 2009 stimulus plan failed to keep unemployment at levels the White House had predicted. The nonpartisan Congressional Budget Office said in late 2009 the stimulus "lowered the unemployment rate by between 0.3 and 0.9 percentage points and increased the number of people employed by between 600,000 and 1.6 million compared with what those values would have been otherwise."

Republican Rep. Jack Kingston of Georgia said his party needs to do a better job of explaining the need for government job cuts.

"The private sector has had to reduce the number of jobs in order to be competitive," he said, "and I think now the public sector is going to have to reduce some of their jobs in order to stay lean, or try to get lean."

Besides, Kingston said, government workers "tend to justify their jobs by coming up with more regulations on the private sector, and that kills jobs."