If members pay any attention to the people they pick up to run their union, then President Carter is in a lot of trouble with the 2.7 million people who run the government for him.

The American Federation of Government Employees, the largest union in the federal establishment, opened its convention here today. Despite the beautiful weather, the wonderfully silly Aloha shirts and relaxed Hawaiian mood, you can cut the political tension with a knife. Much of it is generated by Jimmy Carter, who managed to get this 300,000-member AFL-CIO union to make its first-ever presidential endorsement for him in 1976.

One AFGE official, representing a large professionally oriented agency in Washington said: "I came here for two things -- to get a dues increase so we can get the job done, and to make sure this federation doesn't do anything stupid -- like endorse Carter again."

At least two delegates are wearing black tee-shirts with a white skull and crossbones on them. For the ecologically minded, the message is a puzzling "federal employes, an endangered species." Only persons aware of the bureaucracy's battle with Jimmy Carter get the message.

The Carter aides are hoping that fear of conservative Ronald Reagan will hold the big 8 million federal-military voter bloc in the Democratic column this November. In a close election, the U.S. worker vote could be decisive in states like New York, Texas, California, Ohio, Illinois and, of course, Maryland and Virginia.

Carter aides complain that U.S. personnel misunderstood Carter's true feelings toward them. They blame the press for playing up worker protests against paid parking, pay caps and various "reforms," making it appear that the president's own work force would like to give him a RIF (reduction in force) notice.

The White House also feels that federal workers have been unrealistic in pinning an antibureaucrat tail on the Democratic donkey. Rather, they say, the president and the Congress have been following the mood of the American people who believe that white collare U.S. workers (with an average $21,000-plus a year salary) are overpaid and that their retirement benefits are overly generous.

While the president is trying to streamline the bureaucratic ship of state -- with his brand of civil service and pay reform -- aides to the chief executive know they need every vote they can get. And after two years of punching the bureaucracy, they are in a position now to give a little and maybe win a lot.

The give is the pay raise due this October. Carter advises believe a moderately generous boost could win them friends in the government, without giving too much ammunition to conservatives. Carter originally budgeted a 6.2 percent pay raise but has indicated that a 7.8 percent adjustment is probably more realistic.

AFGE President Kenneth Blaylock, himself up for reelection at this convention, has predicted the president will give federal white collar workers a 9.1 percent raise. Carter is due to make his federal pay proposal sometime this week.

You'll see some action when the pay news comes in from Washington," an officer said. "If it is less than 9.1 percent, you can kiss an endorsement goodbye. Even that won't satisfy the real militants, but most people will probably accept it as realistic, given the times." However if Carter comes in with a lesser amount, or if Congres clears a bill to temporarily trim retirement benefits for U.S.-military retirees, the official said, "All hell could break loose."

More than 1,000 delegates are registered. About half of them represent blue collar workers at defense establishments, people who work as carpenters, or in skilled trades. The rest of the delegates come from white collar locals such as the government's biggest unionized facility, Social Security in Baltimore.

The delegates speak for more than 50 percent of the entire federal work force and AFGE, with 28,000 dues-paying members in metro Washington, is the area's largest union -- public or private.

On Wednesday the union will elect officers. It also will decide whether to cut back on internal politics by giving national officers four-year terms, and approve a controversial dues increase to finance its $11 million annual operation.

The leadership wants a minimum $11 a month dues figure, half of it going to the national office and half to locals. The minimum dues now for AFGE members is $4.10 a month.