A well-dressed woman, crowded to the wall at the Coraopolis Elks hall by voters trying for a better look at Ronald Reagan election eve, was the key to his defeat in the Pennsylvania primary the next day -- and to his chances to become president.

The woman identified herself as a local Republican leader in this lower-middle-income Pittsburgh surburb and said she supports George Bush for president. She had come to the Reagan rally to "pay my respects." But wasn't she worried by the big turnout? "Oh, no. Almost everybody here is a Democrat," she replied, pointing to the unruly throng with seeming distaste. "These people can't vote in our primary tomorrow. Our people are for Bush." "

It was "our people" who kept Bush afloat as a presidental candidate by winning Pennsylvania, where crossover voting is not permitted. The defeat thereby pointed up how much Reagan depends on that Elks hall blue-collar vote in primary states that do permit crossover voting and in November -- more than his right-wing supporters dream and perhaps more than Reagan himself appreciates.

Reagan certainly understands that his advocacy Kemp-Roth tax reduction (a 30 percent cut over three years), through it bothers some of his own advisers, goes over big with working men and women. But he seems to forget how important they are to him when he lapses into reflexive labor-baiting, as he did the day of the Pennsylvania primary.

Bush's Pennsylvania win was based on 3-to-2 margin in Philadelphia's well-heeled, traditionally Republican suburbs, where blue collars are seldom worn. Outspending the nearly bankrupt Reagan campaign better than 12 to 1, Bush successfully appealed to Republicans with a relentless attack on Reagen's Kemp-Roth support as a violation of the classical economics he learned at Yale. The first innovative Republican economic strategy since the New Deal was thereby rejected by Pennsylvania Republican Tuesday.

That is why key Reagan backers in this state privately complain about his plugs for Kemp-Roth. But not Rep. Robert Walker, a populistic conservative who backed Reagan in 1976 when Reagan's present state leadership was saving the state for Gerald Ford. "The blue-collar workers want a tax cut," Walker told us as Reagan visited his district. "It's the economists who have trouble with it." r

Reagan has been 1980's only Republican presidential hopeful who consistently attacks the Carter administration's high taxes and calls for lower taxes across the board. On his last preelection Pennsylvania tour, her triggered stormy applause from Republican audiences at Springfield in the Philadelphia suburbs and at Scranton airport. But his tax-cut pitch seemed to confuse them; it brought only silence.

Not at the Elks hall here. The Democratic-infested audience (many without Republican ties and jackets) cheered Reagan's tax-cut promises before rushing to the fried fish and keg beer. After that rally, Reagan commented to us that one-third of all "working Americans" have entered the 30 percent tax bracket and predicted the number soon "will probably be up to half."

Yet the next morning at St. Mary's College in South Bend, Ind., Reagan seemed to ignore his need to woo those overtaxed "working Americans" when a young questioner asked whether antitrust laws should be applied to organized labor. That was an echo of 20 years ago when right-wing businessmen sought to checkmate labor by outlawing national bargaining.

While tax reduction would surely be high on President Reagan's agenda, antitrust restrictions on labor would not even be discussed. Yet Reagan could not say "no" to this old bromide. He started cautiously, saying that "we should look very closely" at the idea, but later in a press conference endorsed it outright.

"This hurts," one aide confided to us. Reagan had handed labor leaders a weapon to persuade union members that Reagan threatens their paycheck. "I'm sure all the reporters will lead their stories with this," the aide mused. He was wrong; Reagan's defeat in Pennsylvania smoothed out the blunder.

That defeat compels Reagan to stay on the campaign trail against Bush, whose one hope for the nomination is that Reagan will make a colossal blunder under merciless questioning. Yet, with only half a millon dollars (to Bush's $3.5 million) left for primary campaigns, he needs to meet the press for all the free television he can get. Those chance encounters invite disasters.

Reagan's advisers want to whisk him off the campaign trail, away from dangerous questions from newsmen bored with his basis speech, and out to his Santa Barbara ranch for private discussions about general election strategy. That strategy will refine his pitch for blue-collar voters. Ironically, inability of those voters to cross over for him in Pennsylvania prolongs his liability to self-inflicted wounds that could be much more severe than the damage at St. Mary's College.