House Republicans sketched their vision for a smaller federal government Wednesday, proposing sharp spending cuts that would wipe out family planning programs, take 4,500 cops off the street and slice 10 percent from a food program that aids pregnant women and their babies.

Top White House priorities also would come under the knife: Key Republicans are proposing to defund President Obama’s high-speed rail initiative, slash clean energy programs and gut the Office of Science by 20 percent — cuts that would deal a direct blow to Obama’s innovation agenda. They would also cut the Environmental Protection Agency by 17 percent.

Programs traditionally favored by Republicans would not escape unscathed. The list includes significant reductions in agriculture programs, which benefit many GOP districts. All told, House leaders are aiming to cut programs unrelated to national security by more than $40 billion over the next several months, an unprecedented reduction.

“Never before has Congress undertaken a task of this magnitude,” House Appropriations Committee Chairman Harold Rogers (R-Ky.) told Republican lawmakers in a closed-door meeting where he unveiled the proposal. “You will be voting on the largest set of spending cuts in the history of our nation.”

The full impact of the Republican plan was not immediately clear. Rogers released only a partial list of spending decreases measured against Obama’s 2011 budget request, which was never enacted, rather than actual spending levels. He is expected to announce the complete spending plan later this week and present it for debate in the House starting Tuesday.

But even as Rogers warned about the pain his plan would cause, many lawmakers sent to Washington with the support of the small-government tea-party movement were clamoring to cut deeper. Leaders of the conservative Republican Study Committee are vowing an alternative spending plan that would make good on a campaign pledge by House Speaker John Boehner (R-Ohio) and other GOP leaders to reduce government spending this year by at least $100 billion. Republicans leaders dismissed the idea as unrealistic after taking office.

“We still intend to offer an amendment that will meet our $100 billion pledge by setting non-security spending at 2008 levels for the 2011 fiscal year,” said Brian Straessle, the Study Committee spokesman. It was not clear whether the committee would propose cuts to specific programs, or whether it would simply call for spending across the board, avoiding the messy and often painful details.

House GOP leaders endorsed the appropriations cuts but were vague on the details. Boehner said the package would fulfill “our pledge to the American people that we will cut spending. All of this will help create an environment where we’ll have more jobs in America.”

Democrats on Capitol Hill and in the White House argued that the cuts would do just the opposite, undermining the very federal programs that are aimed at creating jobs.

“This Administration strongly agrees that we have to make tough choices to bring down the deficit and get the country back on a sustainable path,” said Kenneth Baer, spokesman for the White House budget office. “But to win the future, we cannot make cuts that undermine our ability to create jobs, drive innovation, and compete in a global economy.”

In the budget request he will deliver to Congress on Monday, Obama plans to include a five-year freeze in non-security spending that would save an estimated $400 billion over the next decade.

Obama will also take aim at some Democratic favorites, according to a source familiar with the budget process, proposing to halve funding for low-income heating assistance. Obama will request $2.57 billion for the program, its level in 2008, before Congress doubled its funding to account for a spike in the price of fuel.

Even as Obama prepares his budget for the coming fiscal year, Republicans are struggling to put together a spending plan for the current one. Congress never approved a budget for the fiscal year that began in September, and government operations are being financed through a temporary resolution that expires March 4. Unless Congress and the White House can agree on a budget for the rest of the fiscal year, they risk triggering a government shutdown.

Republicans are pressing for far deeper cuts than either the White House or the Democrats who control the Senate are willing to accept. In his presentation to fellow Republicans, Rogers said his spending plan would eliminate 60 federal programs entirely, including the Corporation for Public Broadcasting and the AmeriCorps volunteer program, one of President Clinton’s signature creations.

“Make no mistake, these cuts are not low-hanging fruit,” Rogers said in a statement. “These cuts are real and will impact every District across the country — including my own.”