Rep. Robert N. Giaimo (D-Conn.), who is leading the fight in the House to balance the budget, yesterday announced his retirement at the end of this year after 22 years in the House.

Under the rotation rule adopted for the House Budget Committee, Giaimo would have had to give up the chairmanship after this year. The House already had bent the rule last year to let him serve a second two year term. But Giaimo said that isn't the reason he is leaving.

A lot of middle-level members with 20 or 30 years service like Giaimo have been leaving recently. Some say it isn't much fun anymore -- living in a fishbowl, seeing the power of a chairman diluted by reform. Giaimo says he loves the job, but he is tired of having to work here all week as Budget chairman and second-ranking Democrat on the Defense Appropriations subcommittee and then be expected to spend each weekend at home with constituents. At a "healthy 60," he wants to try something else such as practicing law, and perhaps some teaching.

Giaimo was elected to the House in 1958 when a recession caused Connecticut to throw out all six Republican House members and elect Democrats. Giaimo is the only member of that class left. When he and Sen. Abraham Ribicoff (D-Conn.) leave, the state will have no one in Congress with more than 10 years' seniority.

Giaimo said he would have preferred to announce his retirement after the first budget resolution has been disposed of, but felt that because of the "22 years of pent-up demand" among young politicians in his New Haven district waiting to run for the seat he should give them time to get ready. He had set today's presidential primary in his state as his deadline to announce.

Last week, Giaimo succeeded, for the first time since the new process of creating a congressional budget was begun, in getting bipartisan support in the House for the budget resolution setting spending targets for next year. He did that by leading a fight to cut $16 billion in proposals from Presient Carter's request and providing a paper surplus. But in doing so he lost the support of urban liberals who fear their poor will suffer most of the cuts. Giaimo indicated yesterday that he will ask that a House vote on the resolution be put off until after Easter to find out what the Senate Budget Committee will do.

Speaker Thomas P. (Tip) O'Neill Jr., one of the old-fashioned liberals who doesn't want the urban programs cut back, praised Giaimo as "one of the most highly regarded members . . . a real, able, talented solid citizen."

But when asked if he would go along with Giaimo's opposition to putting an urban package back in the budget resolution, O'Neill was quick to reply firmly: "Not me."

After four days of listless debate that engaged only a handful of senators, Majority Leader Robert C. Byrd (D-W.Va.) filed a cloture petition to limit talk on the crude oil tax compromise drafted earlier this year by House and Senate conferees.

His apparent intention is to get Republicans to agree voluntarily today to a vote later this week on the measure, which would raise $227 billion by 1990 from the profits that oil producers will reap from President Carter's decontrol of domestic oil prices.

The House approved the conferees' version of the administration's tax proposal last month, but some Republicans and oil state senators have been pushing to send the bill back to conference to extract a bigger tax break for independent producers. But even they frequently drifted away, prompting Byrd to complain at one point yesterday that only senatorial manners kept the protax majority from whipping the bill through in their absence.