President Carter sent to Congress yesterday his long-promised proposal to overhaul the mystifying federal pay system, a plan that he said would eventually save taxpayers at least $3 billion a year in payroll costs.

While nobody's pay would be cut, the proposal would be expected to hold down future pay raises for about 2 million white and blue collar civilian workers, many of whom Carter and other administration officials have said are overpaid.

The planners do not yet know exactly who would be affected or by how much. But it is likely that the small town federal administrator who outearns the local grocer, or the federal maintenance worker who outearns a beginning college graduate engineer would be among the hardest hit.

On the other hand, a federal secretary in New York City who now makes less than the insurance company clerk up the street could expect an extra raise.

Because the plan gives more emphasis to prevailing local pay standards, informed sources said, indications are that most employes in the high-cost Washington area ranked at GS 13 and below "clearly will benefit" from the changes if Congress approves the plan.

The proposal would not, however, alter the freeze that currently holds the salaries of highest-ranking federal officials, most of them in Washington, far below that of their private sector counterparts.

Federal employes unions, already riled at Carter because of his civil service reforms and other efforts to control the bureaucracy, have been grouping for an all-out fight against the measure on Capitol Hill.

However, the present pay system is in such serious trouble that if Carter's proposal is not approved, federal employes could face even more painful attacks on their paychecks, Alan K. Campbell, director of the U.S. Office of Personnel Management, warned yesterday.

Federal workers are supposed to receive pay comparable to that of their counterparts in the private sector.

However, the pay raise mechanism is subject to both practical and political distortions and is so complex that, as one congressional expert put it, "few people understand the process, and if they did they would probably be horrified."

The cornerstone of the administration's proposed changes is the consideration of fringe benefits and pay, instead of just pay, when comparing private sector compensation with that of federal workers.

"We now ignore the fact that the government's generous pensions and other benefits amount to over 30 percent of the cost" of the federal payroll, an administration official said.

The proposal would also:

Add state and local government workers to the "universe" used for comparison with the federal sector. These workers currently are ignored, even though they have grown in recent years to 13 percent of the total national work force.

Break up the nationwide pay schedule for white collar workers to take into account prevailing local rates. As it is now, the system causes federal workers in New York City to be underpaid, while those in rural Alabama are considerably overpaid, officials said. It also puts pressure on some employers to raise salaries to keep up with the federal competition.

Eliminate several lucrative elements of the current blue collar pay system, which officials said enables some of those workers to make up to 8 percent more than their local private sector counterparts.

Eliminate overtime pay for more than eight hours work in a day, retaining it only for work exceeding 40 hours a week, and make other changes in federal premium pay rules to bring them closer to private sector practices.

Kenneth Blaylock, president of the AFL-CIO-backed American Federation of Government Employees, the largest federal employe union, noted yesterday President Carter for two years has limited federal pay raises to 5.5 percent, short of what the system says is "comparable" to the private sector.

For Carter to ask Congress for even more authority over workers' pay, he said, was "like making Nero the fire chief of Rome."

Rep. Gladys N. Spellman (D-Md.) who chairs a key subcommittee of the House Post Office and Civil Service Committee, warned that the pay proposal "attacks peoples' wallets" and may move federal workers to "stop hiding behind the Hatch Act," and campaign against it in huge numbers.

Rep. Herbert E. Harris II (D-Va.), who represents a large number of federal workers, yesterday urged his congressional colleagues to make sure the plan is "not railroaded through as just another public relations gimmick that makes scapegoats of federal workers."

At the president's request, the proposal will be sponsored in the House by Rep. James M. Hanley (D-N.Y.), chairman of the Post Office and Civil Service Committee, who is generally said to be "lukewarm" to the idea.

The U.S. Chamber of Commerce, a leading critic of the present system, yesterday endorsed the president's proposals, while urging him to go even further.

"In 1977, average federal pay ran workers, resulting in a cost of $10 said Richard Lesher, Chamber president.

Campbell called that comparison "not very meaningful," however. While it is true that private sector employes averaged $12,000 a year compared with $17,000 for federal employes, he said, the government has a much higher proportion of highly paid awyers, engineers, and economists than the private sector. "We believe the gap is less than 42 percent," Campbell added.