GOP seeks no-tax formula.

Walter F. Mondale pushed the tax button during his acceptance speech for the Democratic presidential nomination, and Republicans have been scrambling ever since.

After Mr. Mondale proclaimed that, no matter which party wins, taxes will go up next year, Democrats have had the luxury of sitting back and watching Republicans fight among themselves over whether that was so. At least for the short haul, the Democratic strategy appears to be working.

''We thought we could put them in a tailspin, and we have,'' says a pleased Rep. Tony Coelho of California, chairman of the Democratic Congressional Campaign Committee.

The GOP, the party with the popular incumbent, proved unity, and a booming economy, has dissolved into a dispute just days before its national convention. House members on the party's right wing gathered Thursday to proclaim they would fight, even on the floor of the Dallas convention, for a guarantee of no tax increase.

The focus is ''to insure that the GOP platform has an ironclad plank against tax increases,'' said Rep. Vin Weber (R) of Minnesota.

Shortly afterward, Rep. Trent Lott of Mississippi, chairman of the Republican platform committee, announced that President Reagan ''wants a strong plank'' against tax increases. But the platform chairman doesn't like the word ''ironclad.''

Meanwhile, Republican moderates continue to warn against making rash promises on the tax issue. Rep. Barber Conable of New York, the ranking Republican on the House Ways and Means Committee, calls such proposals ''quixotic,'' since Congress has already passed a law to keep tax rates from keeping up with inflation and so may be forced to increase them.

''I don't think it's inevitable,'' says Mr. Conable, one of his party's top tax experts. He also charges Mondale with ''being manipulative when he says there is a secret (Republican) plan for taxes.''

But Conable says, ''It may be necessary to raise taxes at some time in the future.''

If the tax debate has taken Republicans by surprise, both sides recognize that the issue could turn around before next fall's elections.

Commenting on White House handling of the issue, Rep. Dick Cheney, a conservative Republican from Wyoming, said at a breakfast Thursday, ''It's my impression that they've had a little trouble getting their act together on taxes.'' But he added that candidate Ronald Reagan also stumbled early in his 1980 election by making verbal gaffes, such as those attacking the communist government of China.

Representative Cheney, who served in the White House as President Gerald Ford's chief of staff, predicted that ''people will know by Labor Day that Walter Mondale is for tax increases and Ronald Reagan is against tax increases.''

Congressman Coelho, the Democratic congressional campaign chairman, concedes that the issue could possibly backfire on his party. If the question becomes taxes vs. no taxes, ''we lose'' the debate, he says. ''I think you've got to move the tax thing from raising taxes to fair taxes,'' he says, and he proposes that on the fairness issue the Democrats have the edge.

Coelho and Democratic pollster Peter D. Hart briefed reporters this week on a poll taken in June which they said provided the basis for launching the tax issue. The Hart poll found that while the Republicans still enjoy slight advantages on handling the economy in the view of the public, they have fallen dramatically on the issue of reducing the federal deficit. While the GOP held a 55-to-13 lead in a 1981 Hart poll, the latest finding shows the Democrats scoring a 33 percent favorable rating to 30 percent for the Republicans.

''That's what $200 billion will do for you,'' said Mr. Hart of federal deficit increases under the Republican administration.

Democrats are also taking comfort in a finding that 57 percent of the public now say they ''worry about where things are headed,'' while only 27 percent says they are confident they are ''headed for good times.''

However, Republicans are already preparing the counterpunch to the Democrats on the economy. Although the factions of the GOP may divide over their rhetoric , the message developing is that Mondale represents the no-growth era of the late 1970s.

The GOP right-wing activists, led by Rep. Newt Gingrich of Georgia, are pushing that point even further, calling for an economic plan that would balance the budget chiefly by an expanding economy, low taxes, and spending restraints. ''We tried Walter Mondale's policies,'' Representative Gingrich says. ''It was a disaster.''

''Walter Mondale wants to raise taxes so that spending can go on as usual in Washington,'' charges Rep. Phil Gramm (R) of Texas.