MANCHESTER, N.H. -- The race for the Republican presidential nomination has broken down into two nearly distinct contests: one between Vice President Bush and Sen. Robert J. Dole (Kan.), with the winner likely to capture the nomination, and the other between former television evangelist Pat Robertson and Rep. Jack Kemp (N.Y.), with the winner in a position to become the keeper of the conservative flame, perhaps for years to come.

The Robertson-Kemp showdown, according to party analysts, will help sort out whether the issues that propel conservatism into the 1990s are mainly economic (as they have been throughout the 1980s), or moral and cultural. Under certain circumstances, it could also bear on which of the two party's establishment figures, Bush or Dole, winds up as the 1988 nominee.

If the Bush-Dole battle is protracted, with neither having the strength to knock out the other, a conservative might be in a position to deliver the winning block of delegates at the convention this summer in New Orleans. The Robertson forces already have established a de facto "detente" with Dole campaign; the Kemp campaign has forged alliances with Bush.

Any brokerage scenario is highly speculative. The more immediate piece of business in the "fight for the right" is Tuesday's New Hampshire primary, and it is shaping up as a do-or-die day for Kemp.

His advisers privately concede that if he finishes behind Robertson here -- as he did last week in Iowa -- his candidacy will be moribund. Just a few weeks ago, Kemp, who a decade ago helped turn supply-side economics into national policy, had been surging in the polls in New Hampshire, closing in on Dole. Then came Iowa, and the surge went to Dole and Robertson.

Kemp now finds himself squeezed and losing altitude here. "Jack needs a miracle, no doubt about it," said Dole adviser David Keene. The Washington Post-ABC tracking polls show Kemp, Robertson and former Delaware governor Pierre S. (Pete) du Pont IV (who also needs to finish at least third to keep his campaign alive) all closely bunched, and all well behind Bush and Dole.

Robertson does not have much of a natural base in this state, but he has the most assets among the three for the long haul: money, a deep and energized organization, and good-looking prospects in Minnesota (Feb. 23), South Carolina (March 5) and throughout the South on Super Tuesday (March 8).

The question he faces is whether he can break beyond being the candidate of the "religious right" and establish himself as the standard-bearer of the economic and foreign policy wings of the conservative movement as well.

There is divided opinion among movement leaders on this question -- though, surprisingly, some of Kemp's top supporters are among those who see the most room for Robertson to grow.

"Pat has gone very, very far toward being able to make the claim that he should be the leader of the conservative cause for years to come," said Richard Viguerie, a New Right direct-mail fund-raiser and Kemp supporter. "He has brought energy and passion to the campaign that excites conservatives."

Of Kemp, Viguerie said: "The vast majority of conservatives would say that Kemp has not led on the issues. There is a feeling that he is someone who is too much a creature of the process -- someone who is not comfortable attacking Congress, for example. And I don't don't just mean Teddy Kennedy -- that's too easy. Can you comfortably attack the Republican leadership, {House Minority Leader} Bob Michel, for constantly compromising? Can you be critical of {Secretary of State George P.} Shultz and Bush and {Commerce Secretary C. William} Verity? Pat Robertson feels comfortable taking the conservative position on every single issue, without exception."

Edward J. Rollins, a former White House political director, and now Kemp's campaign chairman, said: "If Robertson is the survivor {over Kemp}, he has the potential to put the next generation of conservatives together. My sense is that he is going to be able to overcome a lot of his negatives in the course of this campaign."

Among the electorate as a whole, and even among conservatives, Robertson's "negatives" go to a queasiness about mixing church and state, about his background as a television evangelist (a term he now bristles at), and to a perception that his moralism is marbled with intolerance. Some think that if he has a high profile at the GOP convention this fall, it will damage the party's chances in November.

"If he insists that the convention spends all its time on abortion, drugs and AIDS, he will be raising the issues that scare younger voters away from the Republican Party," said David Boaz, vice president of the Cato Institute, a conservative, libertarian think tank. "Under Reagan, the Democrats haven't been able to make the 'intolerant' charge against the Republicans stick, but with Robertson, they will."

Robertson's candidacy highlights the core instability in the conservative coalition that produced two landslides for President Reagan this decade. One new element in that coalition was the youth vote, which liked the lower taxes and growth economy promised by supply side economics.

Another was evangelical Christians, who share Robertson's view that the nation's most pressing problem is moral decay and a breakdown of traditional family values. In 1976, 56 percent of the evangelical Christians voted for Jimmy Carter, and he swept the South. In 1980, 60 percent voted for Reagan, and he swept the South, except for Carter's native Georgia. In 1984 and 1986, evangelical Christians voted solidly Republican.

"The South is the critical region in presidential campaigns," said Gary Jarmin, a consultant for Christian Voice, "and it's nonsense to worry about Robertson projecting a right-wing image. The Democrats are likely to have a southerner on their ticket. The Republicans are going to need someone who can mobilize the evangelical vote in that region."

The question that sooner or later every conservative leader asks about Robertson is the same one that was posed about Jesse L. Jackson in 1984 (and may be again in 1988): What does he want?

"I think he wants to fight all the way to the convention and then say: 'Let's talk about the vice presidency,' not for himself but for someone he feels strongly about," said Paul Weyrich, head of the Free Congress Foundation and a sometime Robertson adviser. "And I think he wants assurances on other top level appointments."

"If he goes there with 15 pecent of the delegates, his price might be x," said Viguerie. "If he goes there with 30 percent, his price might be y."

Whatever the bartering, it would go more smoothly with Dole. There has been what Keene called a "detente" between the two camps. "It wasn't negotiated; it just sort of happened."

In his years as a GOP leader, and especially during this campaign, Dole has been careful to put out a welcome mat to evangelical Christians. Bush forces, on the other hand, have gotten into turf wars at the local level with evangelicals, especially during the bloody wars in Michigan, where Kemp wound up bolting from Robertson and allying with Bush.

Weyrich said that Robertson remains "a surprisingly unknown commodity to many secular conservatives" and that, in order for him to become a significant movement leader, he has to show a "long-term seriousness -- not just be a one-time candidate and say goodbye." If he spends the next four years looking over the right shoulder of the president, he said, Robertson could be a formidable political figure into the 1990s.