Republican governors applauded nervously today as President Reagan used his first veto to pressure Congress for further cuts in domestic spending. Some warned that the reductions in federal-aid programs could hurt the GOP politically in 1982, but most said their constituents still support the president's drive to curb the federal budget.

Reagan's pollster, Richard B. Wirthlin, came to the annual meeting of the Republican governors association with the upbeat message that success in the war against inflation can make 1982 a "year of opportunity" for the GOP. But the 20 Republican state executives, most of whom will be on the ballot next year, betrayed strong worries that the recession, rising unemployment and reduced federal aid may throw them a curve in their re-election campaigns.

While conceding that the course of unemployment could be "a very critical determinant," Wirthlin said that if the recovery comes in time for unemployment rates to be falling next September and October, "it will bode very well" for Republican chances. The administration is predicting that the recession will end by late spring or summer, but employment gains often lag behind the turnaround in economic activity.

A more immediate worry of the GOP state executives is the fate of federal aid programs in the sharpening partisan struggle between the White House and Congress.

Their chairman, retiring Virginia Gov. John N. Dalton, applauded the president's veto, but conceded that most of the governors are "concerned about future cuts," because Congress has given the states little flexibility in reprogramming funds for their own priority needs.

The governors, racing to keep up with events in Washington, passed a resolution supporting the veto and calling on Congress to "resume the appropriations process." They bypassed any formal statement on the scale of the domestic program cuts the president is seeking, but many individually expressed misgivings.

Vermont Gov. Richard A. Snelling urged Reagan to slow his budget and tax-cutting drives, saying "the pace may be as much of a problem as the direction is an advantage."

Noting that unemployment in his state has reached 10.6 percent and is predicted to go even higher, Oregon Gov. Victor G. Atiyeh said the thought of new budget cuts was "terrible" and asked Reagan to postpone scheduled tax cuts instead. The call for a postponement of tax cuts also came from Gov. Richard Thornburgh of Pennsylvania. But most of the governors supported the tax cuts and urged Reagan instead to spread the reductions across the government--including defense--instead of concentrating on the discretionary federal-aid programs.

Advocating what he called a "spread-the-misery" approach, Tennessee Gov. Lamar Alexander warned, "You don't cut states this way, you cut people. If there have to be economies, let the defense budget share in the limits on growth."

Wisconsin Gov. Lee S. Dreyfus said that when he and three other Midwest governors saw Reagan last Friday, they urged him to shift $5 billion or $6 billion of planned domestic cuts to the defense side of the budget. Conceding that they had received no encouragement from Reagan, Dreyfus said, "Our purpose was to tell him the depth of the pain we are experiencing" as a result of the recession reducing state revenues at the same time the administration is trimming federal aid.

"This is not just getting our teeth capped," he said. "This is root-canal work, without an anesthetic."

Illinois Gov. James R. Thompson said he warned Reagan that if the GOP loses governorships in 1982 it would also likely lose congressional seats, "and his ability to govern effectively in the last two years of this term could be affected."

Speaking of the focus of the budget cuts on federal aid, Thompson said, "Sometimes, you fall in a trap of trying to take too much out of too little. The political pain may not be worth the dollar savings."

But Thompson and most of the others urged Reagan to "stick to his guns," and Wirthlin said the image of a president battling Congress to curb inflation and spending was a major political asset to Republicans.