IT FINALLY HAPPENED this spring. All at once Republicans felt liberated from the awful baggage Richard Nixon dumped on them as he left town seven years ago. "Who would have thought it?" Sen. Paul Laxalt told a roomful of state party chairmen at the Mayflower last month. "We're clearly through with Watergate. This president has made us a proud party again."

Remarks like this are a measure of the confidence of a party restored to power and prosperity -- and of the degree to which its future depends on Ronald Reagan.

Today's Republicans like to think that Reagan can achieve for their party what Franklin Roosevelt did for his: build an enduring realignment of popular support. But Roosevelt had 12 years in office to secure his party's place. An amended Constitution now limits Reagan to eight, and the chances of his servince even that long are fair at best.

Strategists of the new Republican era are not happy that so much depends onthe continued vitality, good health and longevity of a president already older than any man who ever served. After reviewing all the good news about party preference from a poll done for the Republicans, a member of the polling firm last month defined the party's centra problem: "how to make these gains less dependent on Reagan."

Party professionals have a variety of tools in mind for doing that. But after all the technology of politics has been applied, the question of the Republican future still comes down to who will succeed Reagan and when, a question the Reagan White House has been discouraging anyone from asking.

To keep the question from coming up, White House political adviser Lyn Nofziger all but announced Reagan's candidacy for a second term even before he was inaugurated, and chief of staff James Baker announced ;it again last month. As the chief aide to one potential successor says, "My man can't even appear to be thinking about 1984. The Reagan people are very sensitive about that."

At least part of Alexander Haig's problem with the Reagan inner circle stemmed from this sensitivity -- the secretary's ambitions were taken for granted from the start. George Bush, recognizing the danger early, was careful to avoid it -- even though it meant disappointing some people who had worked in his own presidential campaign. In contrast to Walter Mondale, whose vice presidential office could have staffed a national campaign, Bush has only one political operative on the payroll -- and that one in a secondary post.

Based just on the life expectancy tables -- and assuming nothing happens to Bush himself -- the vice president's chances of becoming president are about 20 percent in their current term, about 40 percent over an eight-year period. These are better odds on becoming president than you could get on anyone else in either party.

Knowing this gets Bush a lot of respect from people around Reagan who may not always have thought much of him. "Who wants to make an enemy of a sitting vice president?"says one of them. "I could be working for him tomorrow."

Unless it comes to him that way, however, the task of completing the Republican realignment will not go to Bush without a struggle.

Bush's base constituency, says one veteran of the last campaign, is the "traditional, preppy types," or, as another puts it, "the ones with green pants and loafers without socks." That constituency has not nominated anyone in a quarter of a century. To win the presidential nomination he failed to win last year, Bush has to get help from the right.

In the far reaches of the Republican Right, Bush's personal ties with the old party establishment and his softness on abortion and the Equal Rights Amendment rule out any deal. Richard Viguerie, landlord and financier of much of that far right corner, says: "Bush can never get right with conservatives."

But there is more to the Republican Right than Viguerie and the social hardliners of the Moral Majority. Bush talks the language of the military hawks from long conviction, and they recognize it. Reporters on Bush's campaign plan shuddered when he once referred to "my friend Somoza," and there were shudders last month among his preppier supporters when he toasted Ferdinand Marcos for his "love of democratic procedures." But, where Bush most needs help in the Republican Party, that kind of thing helps a lot. Human Events editor Tom Winter, who puts out the weekly line for many movement conservatives, sees real hope for the vice president. "There's no problem on foreign policy. On deregulation, Bush believes in it. If he'd only shift on abortion, we could do business."

A man who doesn't have to shift at all to do business with the right is Jack Kemp. He and it have been doing business since he entered politics 14 years ago as an adviser on fitness to the governor of California.

As the congressman today whose name is already stamped on the coming Reagan tax cut, Kemp is on any short list of GOP, Joshuas likely, if Reagan doesn't make it, to lead the party to that promised realignment. Like few others in the party he can attract money, press attention and the workers who know how to make presidential campaigns run.

Talk to anyone in national GOP politics about Kemp, however and the same question comes up. The actual language universally used is somewhat earthier, but it comes down to, "Does he have the nerve?"

Five years ago, when Kemp's mentor, Reagan, ran against President Ford, Kemp watched from the sidelines. Three years ago, when firends showed him a poll and strategy suggesting he could be elected governor of New York, Kemp found one excuse after another until his friends gave up. Two years later they urged him to run for Jacob Javits' Senate seat. More excuses. Even among his friends, there's a feeling the real reason Kemp passes up such opportunities is that he hasn't got the nerve.

Once again this year Kemp has friends urging him to run for governor. He could probably get the Republic nomination with little difficulty. Party and movement fund-raisers roll their eyes when they talk about the money they could raise for such a race. It would be hard to imagine a softer touch, at this time anyway, than the Democratic incumbent, Hugh Carey.

The prize to be won is great. It would place Kemp, a national hero of the Republican Right with supporters throughout the Rocky Mountains and the Sun Belt, atop the Eastern establishment stronghold from which Thomas Dewey and Nelson Rockefeller launched their bids for power.

Whether Kemp stays in the House (where he now ranks third in the party leadership) or takes the gamble on a race for governor, not all Republicans agree that Kemp only neds a little nerve to go all the way. One right-wing consultant says, "I've always questioned his depth. You keep waiting for the hair spray to melt. Maybe he knows his own limits better than the people who keep pushing him."

After Kemp, the right-wing competition for the Republican succession gets fairly broad.

Paul Laxalt is in the picture as a conservative whose purity on every known issue is perfect and as the member of the Reagan inner circle wit the nearest thing to a peer relationship to the president. He was the titular head of Reagan's lat two campaigns and the champion of the Reagan regulars for posts in the administration. He is notoriously the favorite of Mrs. Reagan. "She'd do everything but lick envelopes for his fund-raising letters," says one intimate.

But Laxalt, though a respected member of the Senate club, is thus far only marginally a man of national reputation. He would need to improve on that. Many doubt he could work hard enough. Others wonder if a politician with a long career in high-rolling, permissive Nevada could flourish under the unique scrutiny a candidate for president gets.

Another potential contender from the right, almost certain to find impurities in any other conservatives who run, is Jesse Helms. Helms has spent the last six years trying to hold Reagan himself to the true faith. Since Reagan took office, Helms has been the unsleeping watchman of the right -- trying to protect the administration from moderates and technocrats scheming to divert it from its true mission. Helms is almost sure to challenge Bush if no one else on the right does and possibly if others do.

The Congressional Club, a fund-raising marvel created in his home state of North Carolina, is spoken of with awe in the financial markets of the right. Those familiar with the club's operation talk dizzily of a $50 million and even a $100 million potential for a presidential race by Helms. A race without matching funds, without spending limits.

Aside from money, there is out there in the conservative flatlands a sturdy corps of Helms rooters, people who one conservative leader says "are ready to die for him." Regulars on the right-wing speaking circuit report that, when they mention Helms' name, one part of the audience always goes wild.

None of this adds up to the likelihood of Helms' getting to be president -- or even getting to be the Republican nominee. But a Helms campaign would be sure of money, sure of fanatical workers, sure of a solid showing in the conservative South and Southwest which would complicate any calculations about the eventual succession to Reagan.

Notwithstanding all the White House announcements, it will probably be several years before anyone will really know if the Reagan succession is four years or eight years away, or something in between. But Bush, Kemp, Laxalt and Helms are only a few of the Republicans with friends who are studying the signs, calculating the odds, keeping up the contacts which can make the difference when the eventual struggle breaks out.

Not all the prospective heirs, of course, will be coming from the hard right -- or even the soft right where the vice president dwells. Though Senate Leader Howard Baker astonished most people last year by how lamely he ran for president, no one believes his ambition died in that first attempt. Ambition is also known to be very much alive in another influential moderate, Senate campaign chairman Robert Packwood. And, aside from the established figures in the national party, there are nice-looking, articulate, generally moderate Republican governors all over the landscape -- many of whom, if you searched their hearts, would reveal not only ambition but a lot of calculation on how to take advantage of any opportunities that may arise.

Whoever does succeed Reagan, from the point of view of building that permanent base for the party, it would probably be well if the succession does not come soon. Reagan's own popularity is not yet backed by any solid base in public opinion for his entire program. Many of his most devoted supporters are frank in saying they'd be surprised if that program is an undisputable success. They are counting on their great communicator to make the country believe it is a success.

It has been Reagan's unique talent to keep the many factions of the Republic Party working together and to make the public feel good about the product. The longer this talent continues to operate, and to the degree the country prospers by it, the more likely it is that the Republican numbers will rise further in those public opinion polls. But the real test of how durable a popular base has been built for the party will only be known when the builder himself is gone -- and the struggle to succeed him is settled.