Legislation that has cleared a key House committee to cut federal jobs could have a substantially smaller impact than has been touted by both its sponsors and its critics, according to a congressional analysis.

The Congressional Budget Office on Thursday released a cost estimate of a bill that last month passed the House Oversight and Government Reform Committee seeking to reduce the federal workforce by 10 percent mainly through attrition. The idea has been raised numerous times this year in spending reduction plans. Most recently, a bill offered Wednesday in the House proposed such job cuts as a way to avoid the reductions in spending in 2013 and later that are required because the congressional “supercommittee” failed to produce deficit-cutting recommendations.

Federal employee organizations have denounced such plans as endangering services that federal employees provide, including border protection, care of veterans, food inspection and collection of taxes.

Sponsors say their bills could reduce the workforce by about 200,000 positions over four years through a hiring freeze allowing the replacement of only one employee for every three who separate. However, there would be exceptions. The measure CBO examined would allow the president to exempt positions for reasons including national security concerns or the performance of critical agency mission needs. The reduction would apply only to other positions.

CBO estimated that all but about 710,000 federal jobs — out of a total workforce of some 2.1 million — could be excepted on those grounds and thus would be off-limits. It based that estimate on the positions designated as protected, for similar reasons, from furloughs in any government shutdown caused by a funding lapse. That figure compares with the 800,000 positions that the Obama administration earlier this year said would be subject to such furloughs.

The result, CBO said, is that the reduction in positions could be closer to 70,000, not 200,000. The cuts would save $700 million in salaries and other expenses in the first year and $17.5 billion over five years, it said.

However, it added that the decisions on which jobs to exempt from cuts would rest with the president, and therefore there is uncertainty as to the impact.

The bill further orders cuts in spending on service contracts equal to the amount of savings generated by the job cuts. “However, if payments were shifted from service contracts to another means of acquiring such services (such as by bundling them together with other types of purchases), the savings would be less,” CBO said.

It added that any savings actually would be achieved only if agency budgets were reduced. Without such reductions, “CBO assumes funding for other discretionary programs would fill the gap created by the specific reduction or savings.”