The government would shed about 7,000 jobs a month under the tough hiring freeze President Carter has slapped on most federal agencies.

Carter's anti-inflation program that calls for voluntary wage-price restraints by the private sector, would allow most government operations to till only half of their vacancies. The freeze, officials says, could last for many months.

About 14,000 government jobs become vacant each month. If the 50 percent replacement rule were strictly followed, only half that number of people could be hired each month to rplace emloyes to retire, quit or die.

The Office of Management and Budget will coordinate the job reduction program that has been anticipated in government for months. Many federal agencies stepped up hiring toward the end of summer, so they could get as many replacements on board before the freeze.

The 20,000 cutback Carter referred to in his economic message to the people represents a reduction from the number of federal workers that had been planned for mid-1979. The government now has 2.6 million to 2.8 million full-time, permanent employes. It is those workers and those jobs that are covered by the 50 percent replacement limit.

One major impact of the president's order will be to eliminate all job vacancies - estimated at between 20,000 and 30,000 - in government at the present time.

Many people who have been trying to get federal jobs will be turned away, or put on "hold" until the freeze is lifted. The 50 percent hiring rule is based on the new job picture. "Old" vacancies will no longer be counted, in most cases.

As with any freeze order, exceptions will be allowed. OMB will control them. The thinking at the moment is that each will be viewed carefully by OMB. Most will be disapproved unless they are in the fields of health or safety, and then only if agencies can justifyan exemption for them.

The question is how hard the freeze will be, how long it will last and how easy, or tough, the exemption policy will be applied. During the Johnson administration Congress slapped a "hard" hiring freeze on government. But individual members quickly sought, and got, exemptions for pet programs and "vital" agencies.

In short order, during the 1960s freeze exemptions were made for the Defense Department which had 55 percent of the federal work force. Next came exemptions for the U.S. Postal Service and Veterans Administration, the second and third largest operations. Then the Internal Revenue Service was exempted, and the Federal Aviation Administration. The 1960s freeze finally fizzled when more agencies were exempt than were left under the hiring ban.

Officials say that the 7,000 jobs per month cutback will decline the longer the freeze is on. That is because the federal turnover rate always drops when a freeze is imposed. Workers are less likely to change jobs, try the private sector or even retire. But for the time being anyhow, hiring is cut in half. And because it is frozen at the 50 percent level, instead of a symbolically higher level,experts believe it has a better chance of working and remaining in place longer.

IOUs for Congress: Members of Congress would have their paychecks held up next time they delay paydays for other federal workers under legislative revived by Rep. Newtons Steers (R.Md). Earlier this month thousands of workers in HEW, Labor, ACTION and Interior got half pay because their budgets were held up a in a Senate-House fight over abortions. Steers' bill - if Congress buys it - would make it illegal to pay members of Congress if other federal employe paychecks are delayed. Las Vegas odds-makers won't even touch this one.

Pay Raise: Rep. Joseph Fisher (D-Va.) says President Carter should increase the size of the recent federal military pay raise, to conform with his own economic guidelines for labor and industry. Civil servants got a 5.5 percent boost this month, although government data showed they were due an increase of more than 8 percent.

Fisher say the work force could get nearly 3 percent more and still be in step with the president's inflation fighting program. The White House is likely to play deaf to this one. Most member of Congress won't help. Although they voted to sit out the federal pay raise in this election year, they caught up in 1977 with a $12,900 annual pay boost.