The stock market plunge that coaxed new flexibility from President Reagan on tax increases failed to budge any of the dozen men who want to succeed him.

The five presidential candidates who had been on record as adamantly opposed to new taxes -- Vice President Bush, Rep. Jack Kemp (R-N.Y.), Marion G. (Pat) Robertson, former Delaware governor Pierre S. (Pete) du Pont IV and Alexander M. Haig Jr., all Republicans -- stood their ground last week, and some criticized Reagan for failing to do the same.

The four candidates who had already supported new taxes -- former Arizona governor Bruce Babbitt, Jesse L. Jackson, Sen. Paul Simon (D-Ill.) and Rep. Richard A. Gephardt (D-Mo.), all Democrats -- treated the carnage on Wall Street as fresh evidence that a deficit-reduction package must include additional revenues.

And the remaining three -- Senate Minority Leader Robert J. Dole (R-Kan.), Massachusetts Gov. Michael S. Dukakis (D) and Sen. Albert Gore Jr. (D-Tenn.) -- continued to leave themselves wiggle room on the politically sensitive subject.

The market upheaval is certain to sharpen the fiscal debate in both parties' nomination contests in the weeks ahead, as the candidates watch and comment while Congress and the White House attempt to negotiate a deficit-reduction package that meets, or perhaps exceeds, the $23 billion Gramm-Rudman-Hollings target for the current fiscal year. Of the 12 candidates, none so far has had a more delicate task of political positioning than Bush, who for the second time in four years has found himself zigging on taxes while his president was zagging.

During the 1984 reelection campaign, Bush spent a brief but embarrassing stretch of days opening a crack in the door for new taxes that Reagan kept slamming shut. This year -- with Reagan facing retirement early in 1989 and Bush a leading aspirant for his job -- the roles have reversed.

Bush made his first public comment on the stock market turmoil Thursday in a Miami speech in which he said the solution to the budget deficit is "not to raise taxes; it is to restrain the growth of federal spending." A few hours later in Washington, Reagan opened his news conference by saying that he is prepared to listen to deficit-reduction proposals from Congress that include tax increases.

Several Bush aides sought to play down the differences. "If you listen to what the president said during the question-and-answer part of the press conference, and not just his opening statement, it's clear that they are basically in the same place," said Peter Teeley, campaign communications director for Bush. "Neither wants new taxes."

Teeley added that Bush's blanket opposition to new taxes was intended as a statement about what he would do as president; if Reagan winds up agreeing to a tax increase, Bush, as vice president, will support it as well, Teeley said.

The market turmoil caught Bush at an awkward moment. In his presidential-campaign announcement speech the week before, he had gone out of his way to emphasize that he would not "raise taxes, period" -- perhaps recalling from 1984 that any less emphatic formulation invited endless questions and trouble. But he then lapsed the day after the announcement, answering a hypothetical question in Atlanta by suggesting that there might be some circumstances in which a tax increase was necessary. When that produced a flurry of stories, Bush regrouped and returned to the tougher language.

"To wiggle twice in two weeks would have caused all kinds of problems for him," said Republican consultant Eddie Mahe, "so he was kind of in a box when the Wall Street news hit. If he said he was changing because Reagan was changing, he would have looked like a sycophant until the end of time."

Here is a rundown on the tax positions of the other 11 candidates, based on public statements or interviews last week with The Washington Post.

The Democrats:Babbitt: "All the flim-flam aside, a realistic plan must include both spending cuts and tax increases." He has proposed a consumption tax -- similar to a national sales tax -- that would raise $40 billion to $50 billion a year and means-tested spending cuts that would bring deficit reduction to $80 billion this year, the most ambitious target of all the candidates. He disputed the argument that a tax increase now might trigger a recession. "The best way to avoid a recession is to deal seriously with the deficits," he said, but added that he might be willing to phase his tax plan in over two years. Dukakis: He called for "strong determined measures" and "tough choices" in the wake of Monday's 508-point plunge in the Dow Jones Industrial Average, and he insisted that the "best and fairest" way to raise new revenue is to collect the $110 billion in federal taxes that are owed but not paid each year. He said he would not consider raising taxes without first launching a massive tax-enforcement effort. He also reiterated his call for trimming the Defense Department budget, including all spending for the Midgetman missile. Gephardt: He called for raising $20 billion in new revenues this year, through an oil import fee ($8 billion) and a "base-broadening" Ways and Means Committee tax proposal that would raise $12 billion from corporations and upper-income taxpayers. He called for spending cuts of $10 billion to $20 billion, mainly in farm and defense programs. Gore: He said he favors tax increases "only as a last resort" and prefers first to look for spending cuts of an unspecified amount. Jackson: "This is the end of Ronald Reagan feel-good economics," he said, adding, "We have to convince the market that what we do is real, not smoke and mirrors." He called for a deficit reduction that goes beyond the $23 billion Gramm-Rudman-Hollings target. He said taxes on profitable corporations should be increased and defense spending trimmed. Simon: "Everything must be on the table," he said, echoing the line used by Reagan. He said new revenues should be considered only after spending is cut, but he has proposed considering a tax increase on upper-bracket taxpayers and a cigarette tax increase.

The Republicans: Dole: "First things first; we need to focus on the spending side -- where there is still a lot of work to be done -- before we start talking about tax increases." He opposes "fiddling" with tax rates, but supports new user fees, asset sales and closing loopholes. He proposed $33 billion in deficit reduction this year through a mix of those new revenue sources and an across-the-board spending freeze. Du Pont: "The president should just say 'no' to new taxes," he said. "In my years as governor, I discovered that when you give the legislature the eye of a needle, they drive an 18-wheeler through it. Reagan's going to get a big tax increase bill on his desk, and he's going to be helpless to defend against it." Du Pont has called for a phasing out of farm subsidies, the elimination of 100 "unnecessary" military bases and an end to welfare programs for the able-bodied. Haig: "In this volatile climate, I urge him {Reagan} to reject immediate tax increases . . . . Such actions at this time would threaten a further rapid contraction of liquidity and confidence when our economy has not yet digested the impact of the market's fall." He called for spending cuts in all areas of the budget -- including defense -- of 2 or 3 percent. Kemp: "Under Herbert Hoover, three mistakes turned the Crash of '29 into the Great Depression: tight money, protectionism and a tax increase. We must avoid all three. Recent history shows that Congress uses every penny of a tax increase for higher spending." He called for Congress to adopt an across-the-board spending freeze on domestic programs except Social Security. Robertson: He called for "bold action that will tell the world that the United States has the will and the moral courage to balance its budget and shore up the value of the dollar." He ruled out tax increases, calling instead for cuts in "wasteful spending" on both the domestic and defense side.