The General Accounting Office says the government may have trouble hiring the 178,000 replacements it will need next year unless Congress figures out a way to spare new hires from a paycheck bite of nearly 14 percent that goes into effect in January.

Beginning in 1984 newly hired federal and postal workers will go under Social Security as well as the civil service retirement program. Those employes will have to contribute 7 percent of their gross salaries to the federal pension program in addition to 6.7 percent (on amounts up to about $37,500) for Social Security.

Current federal workers and those hired through the remainder of this year will not be affected by the extension of Social Security. They will continue to pay only the 1.3 percent Medicare tax, and their 7 percent contribution to the retirement fund.

Many federal officials and members of Congress are concerned that the double deductions will hurt the government's chances of getting the best people to replace workers who quit, retire or die.

Legislation is pending in Congress to give new federal workers tax credits for the amounts they contribute to the civil service retirement fund until legislators come up with a supplementary retirement program combining Social Security with a scaled-down federal annuity.

In a report prepared for Sen. William V. Roth Jr. (R-Del.) and Rep. William D. Ford (D-Mich.), the GAO said the effect of the dual contributions could mean "difficulties in recruiting and/or retaining quality individuals." The GAO said it would be especially hard for the government to recruit qualified doctors, engineers and other so-called "special rate" people who are paid higher salaries to keep the government competitive with industry pay rates.

GAO said that last year the government paid $93 million in supplemental, special rates to 34,300 employes in hard-to-fill jobs and in high-cost areas of the country.

The congressional watchdog agency said there are four ways to spare new workers from the dual contributions:

Provide temporary tax credits for those employes.

Do not provide civil service retirement credit for those workers.

Provide temporary civil service retirement without contributions but with a 100 percent Social Security offset against any civil service benefits received.

Make participation in the civil service retirement program voluntary for new workers.

Whatever Congress does, it will have to do it fast. The dual payments for new hires begin in about four months, and that reduction in take-home pay will more than offset the 3 1/2 percent January raise proposed yesterday by President Reagan.