"Tip" O'Neill, a powerful man, dragged himself across the carpeting in the speaker's office when the House recessed last week. He looked like a man who had carried an enormous burden too long.

After the press briefing on the last day, Rep. Thomas P. O'Neill of Massachusetts managed a smile as he dismissed newsmen with, "Thanks. Now go enjoy yourselves." He meant it as much for himself as them.

For Tip, the three-week recess means Cape Cod and golfing and maybe a few runs into Boston where he will swap jokes and stories with admirers from old hangouts like Barry's Corner.

Tip is an Irish politician, which means he is a local, a man who lets his white hair fall across his brow as he wraps a powerful arm around a vote, who would rather talk to Mrs. Murphy on her doorsteps then be on a TV panel show.

Years ago, an Irish politician could easily function in Congress. Loyalty, employing a personal approach that blended warm charm with knuckle-cutting discipline, pulling strings, knifing through the bureaucracy, pleading for the "common man" - all could be accomplished in the House's corridors as well as in Boston's ish wards.

But Congress has changed, and the elements that weary a big man like Tip emerged before Jimmy Carter arrived here, although the Carter White House is quite an obstacle for the likes of an O'Neill. He still likes Carter, especially after a one-to-one session with him. But he is frustrated by the workings of his White House to the point of feeling strong aversion for the place.

What a joy it would have been for O'Neill to have come as speaker to the Kennedy White House or even Lyndon Johnson's. But after struggling dutifully with the Carter men in 1977, and getting a fair amount of legislation passed, the effort became an ordeal in 1978 and blew up when his Boston Irish pal, Robert Griffin, was fired.

O'Neill must also contend with a new breed of independent congressmen who are more coldly pragmatic than warmly Irish. They respond more to polls than party discipline. They know that special-interest groups can cut their votes by 5 percent and thereby defeat them in November. There are far too many bills for them to ponder, and not enough time for the camaradarie where crucial decision can be made.

Altogether, with a perplexing White House, a heavy workload and consequent confusion in scheduling legislation. O'Neill's spirit is sorely tested. But he can still muster a partisan defense and cite victories on the Humphrey-Hawkins bill (largely symbolic), foreign aid, the Turkish arms embargo, extension for ratification of the Equal Rights Amendment and progress on energy and airline deregulation.

But the administration's proposals for "instant" voter registration, federal financing of congressional elections, a consumer-protection agency, common situs picketing, cargo preference and the tax package failed. Moreover, the outlook isn't good for pending priority legislation - civil-service reform, the Department of Education bill and hospital-cost control. All that must be dealt with when Congress comes back after Labor Day. That, and a raft of appropriation bills that might wind up as "continuing resolutions" - the Alka Seltzer for Congress when it tries to eat too much too fast.

Congress will have about a month to settle all this, and then it is a rush to the congressional districts where the record will be defended and attacked, and where Jimmy Carter's name won't be invoked very often. The Republicans will gain seats. They deserve to. Republicans have been a responsible and often effective opposition to the ruling Democrats who outnumber them 2 to 1.

O'Neill knows this, and, as he swings his golf club in the weeks ahead, he might be muttering things under his breath - like why didn't the White House send the tax bill up sooner? And why can't there be a White House guy working with him who understands what politics are? And why do these new young guys in Congress have to be so damned indifferent and independent like a bunch of cats crawling on a fence?

Maybe he'll console himself by reflecting over the fact that only three times since George Gallup starting counting has Congress ever turned up more popular than the president: Once with Truman, once with Nixon and now with Carter. That thought ought to make the cigar taste better on Cape Cod.