By agreeing to a budget summit with Congress in which ''everything is on the table,''President Bush has brought himself face-to-face with a dilemma familiar to every modern president: Should he keep a major campaign promise that was central to his election, or should he yield to the external realities that are pushing him to break that promise?

In George Bush's case, the promise was no new taxes, and the reality is a ballooning federal deficit. The way in which he resolves the dilemma will be a defining event for the Bush presidency, with great implications for his party in the 1990 congressional elections and for his own hopes for reelection in 1992.

The president's campaign promise on taxes was a central pillar of his successful campaign for the Republican nomination and for his general election victory against Michael Dukakis. It came at a time when Mr. Bush was reeling from a third-place finish in the Iowa caucuses while Sen. Robert Dole was looking for a knockout in the New Hampshire primary. The pledge of no new taxes was made with the implication that Sen. Dole would increase taxes to reduce the deficit.

In his acceptance speech at the 1988 Republican Convention, nominee Bush restated that pledge as follows: ''The Congress will push me to raise taxes, and I'll say no, and they'll push, and I'll say no, and they'll push again, and I'll say to them, 'Read my lips: No new taxes.' ''

The promise has been repeated often during the first 15 months of Mr. Bush's presidency. Will it now come back to haunt him? The experience of his predecessors in this regard is instructive.

Franklin D. Roosevelt, in a campaign speech in Pittsburgh shortly before the 1932 election, made an explicit pledge to reduce government spending and balance the budget as a means of curing the Great Depression. As president he did exactly the opposite, vastly increasing spending and the deficit through New Deal programs.

Dwight Eisenhower, campaigning in 1952, when the Korean War was an albatross around the Democrats' neck, made the dramatic pledge, ''I shall go to Korea.'' He did, and an armistice agreement was signed less than a year after he took office.

Lyndon Johnson, on the other hand, made an equally dramatic campaign pledge that he did not fulfill when he promised before the 1964 election that "we are not about to send American boys nine or 10 thousand miles away from home to do what Asian boys ought to be doing for themselves." The huge buildup of American troops in Vietnam after the election began the rupture of public trust that was the undoing of a great president.

No president can fulfill every promise, of course. In the 1976 campaign, Jimmy Carter pledged to remove controls on natural gas and to keep price controls on crude oil. As president, he was forced by real-world pressures from Congress and Western allies to do the opposite, decontrolling crude oil and maintaining controls on natural gas. Ronald Reagan made tax cuts the centerpiece of his presidency, yet signed five tax increases into law, including the biggest tax hike in American history -- in 1982 -- and got away with it.

Although Americans tend to be cynical about campaign promises (a recent New York Times/CBS News poll found 40 percent feeling George Bush never meant it at all when he made his no-new-taxes pledge), presidential candidates do genuinely try to keep them. They realize they create expectations on the part of the public that, if dashed, can undercut the essential trust a president must have to govern effectively. President Truman called such promises a "contract with the American people." The trouble comes when reality gets in the way.

Mr. Bush was able to keep his promise in his first budget cycle in 1989 by a budget agreement with Congress that at least appeared to reach the $100 billion deficit target mandated by the Gramm-Rudman-Hollings Act through a combination of spending cuts, accounting devices and a partial "sequestration" or across-the-board expenditure reductions. The president's proposed fiscal year 1991 budget, submitted this January, likewise appeared to reach the act's $64 billion deficit target without new taxes, although there is a call for $13.9 billion in "new revenues."

But now events have finally forced the White House to revisit the president's deeply felt campaign commitment. A combination of more sluggish economic growth, higher interest rates than originally forecast to service the massive debt, S&L bailout costs that will be more than double the administration's original estimate of $50 billion -- all these threaten to wreak havoc with the GRH targets. The deficit for this fiscal year is likely to be more than $160 billion (even counting the Social Security surplus), not the $100 billion anticipated when the budget deal with Congress was reached. And the president's FY 1991 budget, which projected a need for $37 billion in budget cuts to reach the $64 billion target, will now require some $50 billion to $60 billion in cuts (up to $100 billion if S&L costs are counted against the GRH targets) and between $450 billion and $600 billion over five years.

In January Mr. Bush and his budget director, Richard Darman, could credibly threaten Congress with another sequestration if their own budget suggestions were rejected. But today sequestration is a hollow threat. Like the possibility of dropping the hydrogen bomb to settle a regional dispute, it cannot be used without doing damage wildly beyond any benefit; the depths of the spending cuts would be so great everything from military readiness to airline safety would be at risk.

The president's dilemma is further complicated by the fact that since Reagan used the tax issue to such devastating effect in the 1980 and 1984 presidential campaigns, Republicans have used their opposition to taxes as the defining difference with the Democrats. It is the glue that holds the Republican Party together. With other successful Republican issues such as a strong national defense posture, anticommunism, tough anti-crime stands and abortion blunted (whether by world events, changes in public opinion or new Democratic positions), the anti-tax pledge takes on even greater significance.

What are the lessons for Mr. Bush? First, that the people will forgive a breach in a major campaign commitment if the president can convincingly demonstrate that external circumstances have changed. This is something Mr. Bush thus far has been unwilling to do. Despite the Tonkin Gulf incident, Johnson was never able to make such a case in Vietnam, and it was his undoing. FDR, on the other hand, in a 1936 reelection speech, rejected the humorous advice of his aide Sam Rosenman that he "deny categorically" that he ever made a speech promising to cut spending and instead argued that his increases in federal spending had been required to save the U.S. economy and relieve human suffering. He made his case convincingly, going on to win 42 states.

In George Bush's case, circumstances have indeed changed, but not in ways that are immediately evident to the average citizen. That's why it is essential that if the president does agree to raise taxes, he explain to the people why new circumstances have required it. Otherwise he risks provoking a degree of public cynicism that could be dangerous to his presidency.

The president also needs to extract from Congress certain changes in the budget process to make the process more accountable. This would serve as a justification for his accepting a tax increase in return. Expanding presidential power conferred by the 1974 budget act to rescind individual spending items in overall appropriations bills, gaining the ability to sequester funds midway through a fiscal year -- not just at the outset -- if projected deficit targets will not be met, and obtaining presidential veto power over the congressional budget so he becomes an active player in congressional budget deliberations -- all would strengthen public confidence in a budget process that rarely comes close to meeting its targets.

Last, the people judge presidents by the bottom line. Reagan's popularity, tax increases notwithstanding, was largely a function of an improving economy. Had Vietnam been a victory, Lyndon Johnson would have served two full terms. If a growth-oriented deficit-reduction package, even with tax increases, produces a healthier economy with lower interest rates, less inflation and stronger growth, as it should, there may still be political costs for the Republican Party in the 1990 congressional elections, but all will be forgiven by the time of the 1992 presidential election.

The writer, a Washington lawyer, was President Carter's chief domestic policy adviser in the White House.