The House yesterday approved a budget resolution for next fiscal year, but only after the leadership traded away another bill to win the necessary votes.

The resolution, with a projected deficit of $28.9 billion, squaked through, 212 to 206. Last week, the leadership was embarrassed when a virtually identical resolution was defeated, 213 to 192.

The biggest batch of switched votes yesterday came from Rep. Mendel J. Davis (D-S.C.). He offered House Budget Committee Chairman Robert N. Giaimo (D-Conn.) a switch of 11 votes from no to yes if the House leadership would put off a vote on another bill limiting campaign contributions to House members by assorted political action committees.

Giaimo went promptly to House Speaker Thomas P.( atip) O'Neill Jr. (D-Mass.). Davis delivered.

"When you are in a tight, you use very tool at your disposal that is ethically correct," Davis said in acknolwedging his maneuver.

Rep. David R. Obey (D-Wis.), chairman of the liberal Democratic Study action committee (PAC) bill, issued a statement calling Davis' action "legislative blackmail."

The postponed bill would put a $6,000 limit on gifts to any House candidate by a single PAC, and a $50,000 limit on what a candidate could get from all PACS. The sponsors said they are prepared to raise the latter figure to $70,000.

While O'Neill indicated that the bill would be the first order of business after the recess, Obey bitterly said in an interview, he said in an interview, "In my judgment, the PAC bill is dead."

"If people go home and are accosted and cajoled and arm-twisted, there'll be no bill," he said. "If we can pass it when we come back, then I'm Rumplestiltskin."

The Republican leadership had also threatened the House equivalent of a filibuster to delay next week's Columbus Day recess if the PAC bill were not dropped from the legislative calendar.

A group of liberal members, meaninwhile, who had opposed the budget resolution last week, also switched yesterday. They evidently were convinced that the version proposed by the Budget Committee came closer to setting the spending priorities they favor than would any of the alternatives that likely would have been considered.

In his statement, Obey added, "Nothing could better demonstrate the undue influence of interest group PACS in the legislative process, or the length ot which they will go to maintain that influence. They didn't have the votes, so they engaged in legislative blackmail to buy time."

And buying time was the intent, according to Davis. There was no intent to try to kill the budget resolution, he said, only to postpone action on the other measure on which.not one day of hearings has been held." The House would have voted on it as an amendment to an authorization bill for the Federal Election Commission.

Davis agreed that opponents would use the coming recess to lobby against the bill.

The budget resolution, which covers the fiscal year beginning Monday, calls for outlays of $548.2 billion, revenues of $519.3 billion, and a $28.9 billion deficit.

A conference to settle differences with the Senate on its version of the budget, which provides $2 billion more in defense spending than the House and $4.6 billion less in revenues, is to be held after next week's recess.

Rep. Parren J. Mitchell (D-Md.), one of the liberals who switched their votes, said doing so was "a painful experience for me" because "the priorities in the resolution are still not straight." But he was voting for it, he "now in the first stage of a recession . . . and I've got to look at what is real."

The other potential compromises on the resolution "would put the squeeze to death," the unemployed, he said.

The conference with the Senate may be difficult since the House, during last week's debate, explictly rejected an amendment bringing defense spreading up to the Senate's figure.

All 154 of the House Republicans voting opposed the resolution, including Rep. Marjorie S. Holt (R-Md.). Reps. Beverly B. Byron, Michael D. Barnes and Gladys Noon Spellman, all Mayrland Democrats, supported it. The entire Virginia delegation, including Democratic Reps. Joseph L. Fisher and Herbert E. Harris, opposed it.