Carter administration officials are going to find the going tough when they try to match jobs and pay of federal employes with their counterparts in the private sector.

For the most part, white-collar, federal bureaucrats are urban dwellers. They live and work in high-cost areas. They tend to be better educated and better trained than many of their industry colleagues. And the government now has more scientists and engineers than secretaries.

Although there is a popular push to cut the cost of government and whack the $19,000 salary average of the typical federal employe (it is $22,000 in metropolitan Washington), supporters of pay changes may find stiff resistance on Capitol Hill.

Many people and politicians tend to think of Washington as "the government." Actually, less than 12 percent of federal employes is located here. That is a lot, of course! But there are big concentrations of federal workers in all states. And they represent big voter blocs in a lot of places one would not expect, and in many more that may surprise politicians. Some numbers:

Atlanta has 30,600 federal employes . . . Baltimore, 55,000 . . . Boston, 34,000 . . . Buffalo, 10,000 . . . Albany, 11,000 . . . Charleston (S.C.), 15,000 . . . Chicago, 69,000.

Cincinnati and its Kentucky suburbs have 14,000 U.S. government employes . . . Cleveland, 20,000 . . . Columbus, 12,000 . . . Dallas, 28,000 . . . Dayton, 25,000 . . . Denver, 32,000.

Detroit has 29,000 federal workers . . . Harrisburg, 13,000 . . . Honolulu, 24,000 . . . Houston, 18,000 . . . Huntsville (Ala.), 15,000 . . . Indianapolis, 16,000 . . . Jacksonville, 12,000 . . . Kansas City, 24,000.

Los Angeles, 66,000 federal workers . . . Louisville, 10,000 . . . Macon (Ga.), 17,000 . . . Memphis, 15,000 . . . Miami, 14,000 . . . Milwaukee, 11,000 . . . Minneapolis-St. Paul, 18,000.

The New York City area has over 100,000 federal workers . . . Newark, 22,000 . . . Newport News-Hampton, 10,000 . . . Norfolk-Virginia Beach-Portsmouth, 10,000 . . . Oklahoma City, 28,000.

Philadelphia has 71,000 federal workers . . . Sacramento, 25,000 . . . Phoenix, 12,000 . . . Pittsburgh, 18,000 . . . Portland, Ore., 15,000 . . . Riverside-San Bernardino, Calif., 13,000 . . . Vallejo, Calif., 15,000.

St. Louis has 33,000 federal workers and Salt Lake City, 32,000 . . . San Antonio, 36,000 . . . Tampa-St. Petersburg, 11,000.

Although they have rarely used their muscle, federal workers represent the balance of political power in some counties and cities. In some places they are the city. Military bases create large service industries, but the federal force often is dominant. The largest union in Oklahoma isn't the Teamsters or Oil Workers, it is the American Federation of Government Employes.

If federal workers (and their better organized, more militant postal allies) can get their act together they would represent a potent force. That theme will be pushed by unions - and the gigantic retiree groups - who are worried about coming assaults on their pay system and pension program.

When the numbers are tallied on Capitol Hill, the day may come when Washington area senators and members of Congress aren't the only people who feel it wise to stroke, rather than beat, the bureaucracy at election time.