The Reagan administration may unwittingly succeed in doing something that has eluded the best union organizers: uniting the big federal fraternity, which many politicians consider a timid collection of politically impotent drones, into a bloc that could help elect or defeat nearly half the Congress.

In the process of trimming things federal--like pay, jobs and annuities--the White House has adopted a rather heavy-handed approach that may create a Frankenstein's monster for Republicans and conservative Democrats at election time.

Unless the Democrats nominate John Travolta for president in 1984, the Republican candidate can, for instance, probably kiss off the votes of 2 million federal and military retirees who mostly voted Republican last time.

President Reagan lost credibility with the gray power crowd (which has a big, big voter turnout) when he did an about-face on his preelection program not to mess with their twice-yearly cost-of-living raises. They now get one less raise a year than they did before the election.

Now the administration wants to cut the size of future raises for retirees. It would peg them to either the inflation rate or the percentage increase in federal pay, whichever is less. Under that system, retirees who got an 8.7 percent raise this month would have been limited to the 4.8 percent adjustment that government workers got last October.

If Congress buys the plan this year, and if Sen. Jesse Helms (R-N.C.) has his way, the next raise for federal workers and retirees would be zero. Helms believes that members of Congress (who get more than $60,000 a year in salary and extensive opportunities for speaking fees, plus a $20,000-per-year tax break) could take a 5 percent pay cut so it would be easier to face the voters after sharply limiting Social Security and other federal increases this year.

The nation's 2.6 million federal workers, hit with rare layoffs, furloughs and downgradings, are unhappy with the 5 percent raise President Reagan plans to give them this October. They are less thrilled with the Helms plan--not yet in the form of a bill--to skip any raise this year.

Reagan did turn the hot water back on in government bathrooms, and he removed the toll booths from Jimmy Carter's pay parking lots, thrilling, briefly, drivers and carpoolers who were outraged at being charged an average $15 per month to park at the office.

But memories are short. Those two goodies have been long forgotten by civil servants who--right or wrong--feel this administration is covering them with mud in its attempts to sell Congress and the public on spending cuts for nondefense items.

There are 300,000 federal workers in California (nearly as many retirees) and nearly 150,000 active and retired federal workers in Florida.

New York State has 170,000 active federal workers; Pennsylvania 130,000; Texas, 151,000, and so it goes. A number of states, Alabama, Colorado, Massachusetts, Michigan, Missouri, New Jersey, Oklahoma, Tennessee and Washington, have over 50,000 federal workers each, plus many U.S. retirees. Ohio has more than 100,000 federal workers, as do Maryland (130,000) and Virginia (140,000) and the District of Columbia, more than 180,000. None of those totals include retirees either.

Union membership among federal employes--which has been sagging in recent years--is picking up.

The National Association of Retired Federal Employees, which only recently raised annual dues of its frugal half million members to $9, picked up nearly $800,000 in 21 days when it appealed for funds to help fight further cutbacks in retirement benefits.

Federal and postal unions, which traditionally have had to resort to gimmicks, raffles and turkey shoots to raise a few bucks for political action war chests, say--and their books reflect it--that the money is rolling in.

Put the feds, family members and retirees together, give them common concerns--jobs, pay, pensions--and you've got a large minority group on your hands. Or in your hair! If they start pulling the voting levers in unison, there could be lots of address changes in next years' Congressional Directory.