In a flurry of recrimination that by day's end began to resemble the back-and-forth of a tennis match, Democrats and Republicans including President Reagan traded volleys yesterday over the House's failure to pass a budget resolution last week.

Commerce Secretary Malcolm Baldrige entered the fray, accusing the House Democratic leadership of sabotaging the economy just as it was poised to recover, and Reagan made the budget the subject of his weekly radio talk as the administration sought to keep the political pot boiling during the long Memorial Day weekend when members of Congress will be in their home districts.

In a morning news conference, Republican National Committee Chairman Richard Richards called House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and his allies "ingrates" and accused the Democrats of wanting to see Reaganomics fail "for political advantage."

Richards announced formation of a special campaign unit to defeat the Democratic leadership. He warned that his party would stop "pussyfooting around" and "take off the gloves and start punching back at the Democrats."

Rep. Tony Coelho (D-Calif.), the House Democrats' chief campaign money-raiser, responding to Richards' attack on O'Neill, said the Republicans "are in panic" and "looking for a scapegoat."

But to target opponents of the Reagan budget would mean including Republicans who voted unanimously against it in the Senate Budget Committee and in the House GOP leadership who refused to bring it to the floor, Coelho said.

"Last year Republicans voted in lockstep," Coelho said. "This year the robots are rebelling."

Baldrige, who issued a statement in the morning accusing the Democrats of thwarting an economic recovery, added later in a telephone interview that "it's going to come back to haunt the Democrats unless we do get strong enough action to reduce deficits and bring confidence back to financial markets."

In his weekly radio show, Reagan repeated his charges that the budget-making process was a "ridiculous procedure." He said the House Democrats simply ignored his budget proposals and "preferred to play politics" rather than cooperate in passing a spending plan.

He added that "we'll keep on fighting to get a responsible budget which protects your tax cut and provides for a strong defense program."

Sen. Dale Bumpers (D-Ark.), giving the official response to Reagan's address, said it was the Republicans who had first rejected the president's budget proposals. He said Reagan should "extend the right hand of conciliation," claiming that the American people "are frightened to the point of panic" with "their first brush with an economic nightmare."

Coelho, in his response to Richards, said, "The president's political advisers are obviously hoping to blame Democrats in 1982. But Democrats opposed the program in 1981. The difference this year is the Republicans themselves lack confidence in the president's economic policies."

It was clear the administration's sniping at O'Neill and the Democrats was planned. Baldrige said, in answer to a question, that "I was asked if I was going to say anything about the House budget resolution failure , to say it before the weekend . . . . You could call it a coordinated attack."

GOP pollster Richard Wirthlin, who accompanied Reagan to California, told reporters on the plane that his research shows that six of 10 persons blame Congress for the budget stalemate, while only two of 10 blame Reagan. "If you ask people who's responsible for the economic diffuculty, the Democrats still carry the burden," he said.

In his speech yesterday, Reagan said signs of a turnaround are becoming more evident. "We are starting to get encouraging news from those economic statistics that pour out of Washington," he said, citing the drop in inflation and some downward movement in interest rates.

"Serious problems remain, such as the need for a new budget, and above all unemployment here and in Europe where it's at record levels. But we're making economic headway . . . . "