The White House and Senate Democrats are at a standoff over a key appointment to the Federal Election Commission. The Democrats want President Reagan to reappoint Commissioner Thomas E. Harris to a third term. And traditionally, presidents have honored the choice of congressional Democrats for a Democratic seat on the FEC.

But Reagan is balking at Harris. Congressional liaison Max L. Friedersdorf informed Senate Minority Leader Robert C. Byrd (D-W.Va.) on July 12 that Reagan would not reappoint Harris, but promised a nominee of "impeccable Democratic credentials," congressional sources say. Harris, who was associate general counsel of the AFL-CIO from 1955 to '75, has the strong backing of organized labor, but the National Right to Work Committee has been lobbying against his reappointment.

Reagan's choice hasn't been announced, but the Democrats say they think the president will soon give a recess appointment to former representative L.H. Fountain (D-N.C.), which would allow him to serve through the 1986 election. Democratic Party sources fret that Fountain would side with GOP commissioners on some key votes, giving Republicans a dominant voice on the panel.

The Senate Democratic leadership -- Byrd, Alan Cranston of California, Daniel K. Inouye of Hawaii, Wendell H. Ford of Kentucky and George J. Mitchell of Maine -- wrote Reagan last week, offering him a list of choices. In addition to Harris, they proposed Deborah McFarland, a former FEC attorney who is now executive director of the California Democratic congressional delegation, and Bruce H. Turnbull, a lawyer and fundraiser for Cranston.

The five senators also reminded Reagan that Republicans in Congress "fought long and hard" to prevent President Jimmy Carter from imposing an FEC appointment on them that they did not want. The Democrats pointed out that the Republicans established their "right to participate" back then by sending the president a list, just as the Democrats are now giving Reagan.

Last week, Reagan filled a Republican seat on the FEC, appointing Thomas J. Josefiak to succeed Frank P. Reiche. Josefiak is a former legal counsel for the National Republican Congressional Committee.

WHO'S ON FIRST? . . . Chief of staff Donald T. Regan has carved out a big role for himself in the second Reagan term, one that has many subordinates wondering how well things will operate when the president leaves on his California vacation.

Aides say the chief of staff will spend four or five days in Santa Barbara, then head off for his own vacation, leaving lieutenants in charge on a rotating basis for a few weeks.

BACK TO SCHOOL . . . White House officials are increasingly worried about political and legislative problems that may confront Reagan when he comes home from Rancho del Cielo after Labor Day.

One aide predicts a "hellacious" September with the deficit, taxes and U.S.-Soviet affairs. One trouble spot: legislation to raise the debt ceiling over $2 trillion. There may be difficult appropriations fights as well, and in the midst of it all Reagan wants to hit the road again to campaign for his tax overhaul plan. Federal Trade Commission Chairman James C. Miller III may not be confirmed as Office of Management and Budget director until late September or October, officials say.

A JOB FOR DEVINE? . . . Does the White House have a job for Donald J. Devine, the former Office of Personnel Management director whose confirmation to a second term foundered in the Senate? There's talk of an ambassadorship to the Bahamas for Devine, a longtime Reagan supporter who this week was appointed interim chief of the political action committee of Senate Majority Leader Robert J. Dole (R-Kan.). It's not known if the White House wants to give Devine the diplomatic post.