A new administration is about to take power in Washington and, as it does, world financial markets join a chorus of domestic experts in warning us that we have to deal with our huge federal budget deficits.

President-elect Bush was chosen by the American people to lead the way. He won with a campaign commitment to use a flexible freeze and no new taxes to narrow the deficit. Now, many political leaders and economists are urging him to abandon his "no tax" pledge to help deal with the deficit, but Bush insists that he has a mandate to avoid tax increases.It seems to me perfectly appropriate for him to insist that the position he took in the campaign is one he should live with; at least, for a while.

We should let Bush have his flexible freeze - say for a year, while maintaining the priorities of a strong defense and a "kinder, gentler nation," which both Congress and the president-elect have a mandate to insure.

If he is right, the freeze, plus economic growth, plus a possible drop in interest rates, could combine to reduce the deficit to within the targets established under the Gramm-Rudman-Hollings budget law.

But what happens if those deficit-reduction targets are not reached? Right now, the only fallback is the feared meat ax of Gramm-Rudman-Hollings: automatic, across the board cuts drawn equally from defense and domestic programs.

That may sound effective in theory, but recent history unequivocally says it's not. In 1987, Gramm-Rudman-Hollings threatened such deep cuts that the President and Congress dodged the bullet by adjusting the law's budget targets.

In other years, automatic cuts were avoided through accounting gimmicks and unrealistically rosy assumptions. As it now stands, Gramm-Rudman-Hollings is not a realistic hedge against Bush's bet on the flexible freeze.

But it can be made realistic. If the flexible freeze can't narrow the deficit - and since we apparently won't accept closing the deficit with automatic cuts alone - we should modify the Gramm-Rudman-Hollings trigger.

To wit: Require equal cuts in defense and domestic programs to make up half of the deficit but insist on new revenues to make up the remaining half.

We would thus spread the pain as thinly and evenly as possible but make the political embarrassment of higher taxes great enough to spur Congress and the president to responsible deficit reduction.

Why should President-elect Bush agree to such a plan? For one thing, it gives him leverage to make his flexible freeze work with congressional Democrats. If the Bush budget genuinely and fairly were to meet the law's deficit targets, then Congress would have to bear responsibility for any tax increases if members unreasonably stymied the budget negotiations.

And because Mr. Bush's "no new taxes" campaign commitment was based on the assumption that the freeze would work, his acceptance of this amendment to Gramm-Rudman- Hollings would become a show of confidence in the freeze rather than an abrogation of his "no new taxes" pledge.

The advantages are clear enough. But why should congressional Democrats support a trigger tax? For one important reason: The threat, under the existing Gramm-Rudman-Hollings, of dramatic cuts in vital domestic programs such as environmental protection, education and the fights against drugs and AIDS, as well as in our military preparedness.

A trigger tax, in short, would create a more powerful incentive for all sides to look for a reasonable budget compromise.

(Mario M. Cuomo is governor of New York State.)