House Republicans met yesterday with the director of the Office of Management and Budget to straighten out a few things among themselves about President Reagan's proposed budget and perhaps offset publicity accorded Democrats who held nationwide budget hearings last week.

"The businesslike attitude of our Republican members, including their willingness to work on a holiday, contrasts sharply with the costly and blatantly political tour that the House Budget Democrats conducted over the recess," Rep. Lynn M. Martin (R-Ill.) said in a statement on the Washington's Birthday holiday.

"I am sure that our members learned more about what the American people want from the budget by talking to our own constituents during the recess than did the Democrats by traveling from city to city at taxpayer expense, trying to dredge up witnesses to criticize the president's proposals," she said.

"This meeting wouldn't have been called," said Gene Doherty, Martin's press secretary, "unless the members thought there was an important reason to cut short their recess. There's a lot the Republicans are going to have to get straight among themselves." Congress returns to work today after a weeklong recess.

At a "photo opportunity" an hour into yesterday's session with six Republican House Budget Committee members, OMB Director James C. Miller III, tie loosened, reiterated points stressed during presentations to Congress and journalists.

The budget contains $38 billion in deficit reductions, but only $22 billion of this comes from "reductions in domestic programs," he said. This is only about 5 percent of the $418 billion Reagan has not put off-limits to budget cutters, he added. "This gives rise to the president's statement that, if we can't find a nickel on the dollar that we can cut, we're not really doing our job," he said.

Meanwhile, in Bal Harbour, Fla., House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) briefed the AFL-CIO's 35-member executive board on what he called "the year of the budget." He said Reagan must propose a tax increase or "his defense buildup is over."

By next summer, O'Neill said, "the president will be facing the prospect of the end of his defense buildup or the end of his stand against increased revenues." A tax increase is inevitable, he said, "but it's going to have to come from the president."

"The Republican members of the Budget Committee are so embarrassed by the president's budget they have not showed up at any of the hearings," he said, referring to the Democrats' budget tour.

In reaction, Martin said, "The word 'embarrassed' never occurred to me." House Minority Leader Robert H. Michel (R-Ill.) said, however, it was "not unexpected to hear from the other side."