White House bean counters would have to keep closer tabs on the number of federal employees on the government payroll if a Republican proposal to trim the federal workforce advances.

Three leading House Republicans detailed plans Monday to replace every three employees who depart federal agencies with only one new hire, in hopes of trimming the workforce by 10 percent by 2015 and fulfilling a key element of the House GOP’s 2012 budget plans.

The proposal, unveiled by House Oversight and Government Reform Committee Chairman Darrell Issa of California and Reps. Dennis Ross of Florida and Jason Chaffetz of Utah, details how Republicans propose to achieve that 10 percent cut. The idea stems from President Obama’s bipartisan fiscal commission and was adopted by House Budget Committee Chairman Paul Ryan (R-Wis.) as part of his wide-ranging budget plan.

Issa, Ross and Chaffetz said their proposal would save an estimated $127.5 billion over 10 years.

If passed, the legislation would require the Office of Management and Budget to track the size of the federal workforce on a quarterly basis and report to Congress in writing if the number of employees exceededs 90 percent of its current size in fiscal 2011. No agency would be permitted to fill job vacancies once the limit was exceeded. Agency employees would be tallied on a full-time equivalent basis, according to the legislation.

Under the bill, the president would be able to permit hiring above the legal limit in cases of war, national security concerns or national emergencies.

And in a key concession to federal worker unions concerned that curtailing federal hires would lead to a wave of government service contracts, the bill would prohibit agencies from signing new service contracts because of the workforce limitations unless cost comparisons demonstrated the government would save money.

Though the federal government employs more people than it did in the 1960s, the federal workforce is at its lowest level since then as a percentage of the U.S. population, according to government statistics.

In 2010, federal agencies employed an estimated 2.65 million workers — including Postal Service employees and temporary U.S. Census Bureau hires — meaning there were an estimated 8.4 federal employees for every 1,000 Americans. Forty years ago, the government employed about 2.94 million people — including census workers — or 14.4 of every 1,000 Americans.

Ross, who chairs a House subcommittee on the federal workforce, said government statistics suggest about 400,000 federal workers are eligible for retirement. “As these workers leave, we cannot let this opportunity to save taxpayer money pass,” he said Monday.

But Colleen M. Kelley, president of the National Treasury Employees Union, called the plan “a short-sighted proposal that would only undermine the federal government’s ability to deliver vital services.”

In a statement, she said any exemption for new contracts is “an enormous loophole” that should not be permitted.

Democratic lawmakers also voiced concerns. Rep. James P. Moran (D-Va.), whose Northern Virginia district is home to more than 65,000 federal employees, said that “indiscriminately slashing federal jobs to meet an arbitrary quota is counterproductive and damages the government’s ability to provide for its citizens.”