New Hampshire is faced with the unhappy prospect of either losing its monopoly on having the nation's first presidential primary or being the first state whose delegates will not be seated and voting at the 1984 Democratic National Convention.

The problem is that neighboring Vermont is planning to hold its 1984 presidential primary on its traditional Town Meeting Day, when voters pass on everything from school budgets to nuclear-freeze referendums. For more than a century, Vermont's Town Meeting Day has been the first Tuesday in March. Next year that is March 6, the day earmarked for the New Hampshire primary.

Rather than share the spotlight if Vermont proceeds as scheduled, New Hampshire political leaders said they are prepared to sacrifice their 25 delegates to the 1984 Democratic nominating convention by holding the primary a week earlier--or more if necessary--in defiance of national Democratic Party rules.

In the past, states whose presidential delegation selection process has been out of compliance with national rules have been forgiven on grounds that the state parties had made every effort to have state legislatures change the laws. National party officials said such tolerance is exhausted.

"In the past, the rules have been haggled like an Oriental rug bazaar," said Ann Lewis, political director of the Democratic National Committee. "But [DNC Chairman] Chuck Manatt is not a rug peddler. He's a banker, and he thinks rules are meant to be followed."

Politicians in the two states appear to be unmoved.

"We'll find a way for New Hampshire to maintain the first-in-the-nation primary even if we have to hold it on the Fourth of July of the previous year," New Hampshire House Minority Leader Chris Spirou, a Democrat, vowed.

With an equal touch of Yankee stubbornness, Vermont politicians said there is no way they will reschedule Town Meeting Day to accommodate New Hampshire.

"Town Meeting Day will not change until the earth blows up," Vermont House Majority Leader Stephen A. Morse declared.

This clash between entrenched New England traditions arose because the DNC lopped five weeks off the primary season in an effort to shorten the presidential campaign marathon.

Last year, the committee set a "window" of March 13 to June 12 for states to hold primaries or party caucuses for selection of convention delegates. It gave special exemptions of one week to New Hampshire and 15 days to Iowa, whose caucuses have already stolen some of New Hampshire's political thunder.

The rules, however, do not cover nonbinding "beauty contest" primaries such as Vermont's election. That exception allows Vermont to hold its primary outside the "window" period and on the same day as that in New Hampshire. The conflict was overlooked during the scheduling process.

Being first is important to New Hampshire not just because its voters have become accustomed to first-hand contact with the candidates, but because the invading army of politicians and press pumps millions of dollars into the state economy.

"No one's going to make us come after somebody else," said New Hampshire Democratic Party Chairman Richard E. Boyer, who is to discuss the issue today with Manatt. "We will be first. Public sentiment is that strong," Boyer said.

So strong, in fact, that discussion of a regional primary in 1976 spurred New Hampshire to pass a law mandating that its primary be held a week before any other. Bills making clear that the law includes nonbinding primaries such as the one in Vermont have already been introduced in the state legislature.

While New Hampshire might be able to evade the "window" itself by making its primary nonbinding, leaders of both parties here are unenthusiastic about the idea.

"I don't think the New Hampshire legislature and the New Hampshire Republican Party are going to be dictated to by the Democratic National Committee," House Majority Leader John B. Tucker said.

But they are worried that Vermont may be just "the first crack in the dam," as Boyer put it, and that other states will follow suit with early nonbinding primaries that would undercut New Hampshire's position as front-runner.