Among the 74 new members elected to the U.S. House of Representatives last November were 29 state legislators. Twenty-eight of them gave up their statehouse seats when they took up their new duties in Washington. Then there is Harold Washington.

Washington, a Chicago Democrat, was sworn in as a congressman with the other freshmen this month, but he has refused to give up his seat in the Illinois Senate. The result is a constitutional quagmire that has prompted a Republican coup and furious legal battles in Springfield and a budding effort here in Washington to kick the freshman out of Congress.

Rep./Sen. Washington is aware of the turmoil his unusual stance has caused, but he says he is a victim of circumstances. The circumstances, he says, were brought about by two of his chief enemies in the Byzantine world of Chicago Democratic politics -- Jane Byrne and James (Bulljive) Taylor.

The 58-year-old Washington has built his political career on opposition to the Chicago Democratic machine constructed by the late Richard J. Daley and now run, more or less, by Major Jane Byrne. He was elected to the state Senate on an antimachine ticket, and last spring he trounced Byrne's candidate to win the Democratic congressional nomination in his South Side district. He won the general election with a majority typical for Chicago Democrats -- 95 percent of the vote.

At that point, Washington says, he was prepared to resign his legislative seat and focus on Congress. But then he learned that Byrne was lobbying precinct leaders in his district to give his Senate seat to Bulljive Taylor. Taylor, a member of the state house of Representatives who also holds a $70,000 job on Byrne's staff, is a strong ally of the mayor and a strong adversary of Harold Washington.

To prevent Taylor from filling the Senate vacancy, Washington decided not to create a vacancy. He simply refused to give up his Senate seat, even after he took his House seat here. The congressman has stop taking his Senate salary, however, and he says "I shall do no duties whatsoever in connection with the Senate seat."

This policy caused no particular trouble in Springfield until Thursday, when the Illinois Senate met to open its 1981 session. The Democrats have a 30-to-29 majority, and normally they would have elected their own members to all controlling positions. But one Democrat has been hospitalized, and when Washington refused to attend, Republicans found themselves in the majority, 29 to 28.

The result -- described by The Chicago Tribune as "a stunning power grab" -- was a series of votes engineered by Republican Gov. James Thompson in which the Republicans elected their own members to the Senate presidency and all other manjority slots. Since the GOP also controls the House, Republicans now claim control of the full legislature -- for a session that will redraw the state's congressional and legislative districts.

"Illegal and invalid," the leader of the Senate Democrats declared, he promised to proceed to state court posthaste to challenge the constitutionality of the whole affair. Republicans promised to sue right back to defend their position. Short of this, however, it is possible that if the Democrats can find a senator who is acceptable to Rep. Washington, and the ill senator recovers his health, the Democrats might be able to reassert control in the Senate without legal action.

Meanwhile, back in washington, D.C., another Illinois Republican, House Minority Leader Robert Michel, says he is contemplating a formal move to declare Rep. Washington's congressional seat vacant. Mike Johnson, a Michel aide who has been researching the multivolume "Precedents of the House" for his boss, cites the case of George L. Lilley, who lost his House seat when he was elected governor of Connecticut in 1908 and tried to keep both jobs.

Meanwhile, back in Chicago, Rep./Sen. Washington arranged a series of meetings to try to resolve the dilemma. "I will resign from the Senate at the earliest propitius moment," he declared, but could not say when that might be.