At breakfast the other morning, Republican Sen. Bob Dole of Kansas told reporters he had addressed the sheet metal workers' union in New York on August 30 -- the first time he had ever talked to a labor union group. "And nobody left," he smiled.

The union invitation to Dole, the architect of the compromise tax bill bitterly opposed by right-wing Republicans as a rejection of "supply-side" principles, was a symbol of the new and high regard in which Dole is now held by Democrats, liberals and nonpartisan admirers of his common sense and considerable tactical skill as a legislator.

Dole is only one of a small group of powerful "Establishment" senators who managed to convince the president that he had to back off ideology, and recognize the valid complaint of financial markets that the country was going broke: with ever-rising deficits there would be no hope of turning interest rates downward.

Washington now buzzes with talk of Dole as a Republican presidential candidate, and Dole is doing nothing to discourage it. Israeli diplomats, always alert to change, have made discreet inquiries among friends about Dole -- and of course, about his views on Israel. (I put the question to him, and he answered: "I've always had close ties to Israel, but I don't think we can give a blank check to Prime Minister Menachem Begin.")

Dole is obviously enjoying the new attention he's getting. He told the sheet metal workers that the "only other union I've ever talked to was the Womens Christian Temperance Union, and I think they may have had second thoughts about me." And since he followed Sen. Ted Kennedy to the podium, Dole joshed that for the labor audience, his own appearance "must be like Tugboat Annie following the Queen Mary."

Dole went from the union meeting to the New York Stock Exchange, where he was accorded a hero's welcome on the floor by admiring brokers and specialists. Although many businessmen have been angered because their tax benefits have been cut and some loopholes closed, the brokers said that the stock market rise was in good part a response to the tax bill. They took it as evidence that Congress could act responsibly -- something they had begun to doubt. Witnesses say few politicians have ever been so lionized by the brokers.

When Washington talks of a "New Dole," it is less a reference to a changed ideology than a turn-around in style: as the vice-presidential candidate during the Ford 1976 campaign, he was assigned the low road, and took it -- with apparent relish -- slashing away at his opponents. His nasty tactics that year are not entirely forgotten by Democrats.

But so much praise has come Dole's way not only for seeing the virtues of cutting back the horrendous federal budget deficit, but for putting through some tax reforms that for years had been high on Democratic tax-reformers' lists, that he is just a bit embarrassed.

"I am not a liberal, neither am I a lemming," he felt constrained to write in a Washington Post op-ed piece at the peak of the fight over the tax bill. "We are not making a U-turn, we are merely adjusting the route to keep from going off the road." For those looking for "an ideological litmus test," he cited his rating by Congressional Quarterly for votes reflecting Republican Party unity. At 94 percent it was the highest in the Senate, and far above that of his most severe critic and possible rival for a presidential nomination, New York Rep. Jack Kemp.

Whatever the past, the hard-working Dole does in fact evoke a new image. To reporters at breakfast, he talked with candor about the need for "fairness and equity" in the tax system. He wrote in The Post that "I have never defined conservatism as the religion of the propertied few, or of those whose voice carries in direct proportion to their wealth."

He says there must be more spending reductions, including cuts in defense, "which can't be a scapegoat or a fiscal hog." And the Social Security system is in such bad shape that he is arguing for a special session, after the election, to reduce the inflation-adjustment formula that is breaking the system.

"There is a window of opportunity" to deal with the Social Security problem between Thanksgiving and Christmas, "when even politicians are not too political."

What reporters like about Dole is that he's accessible and doesn't kid around: he talks straight. On "Meet the Press" recently, when asked if the 1981 tax bill hadn't been too much of a good thing, Dole said:

"I never really understood all that supply side business."

Asked to assess former Republican National Committee Chairman Bill Brock's prediction that the GOP might actually show a net gain in House seats in the November election, he quipped:

"I think that's a carryover from (his) having been national chairman. They're always optimistic."

On the question of a "flat tax," on which his Senate Finance Committee will soon hold hearings, Dole said that "instead of a phrase, we ought to understand what we're talking about. They talk about it a lot on (TV) talk shows, especially in California -- but they have a lot of different ideas in California."

Can this country ever deal with its deficit problem?

"I wonder about that all the time," Dole confessed. "The longer I'm here (in Washington), I wonder how we've kept everything together!"