MANCHESTER -- The first stage of the Republican presidential fight here -- the battle for the backing of the state's top party officials and for the support of its key GOP activists -- is quietly coming to an end.

"The pool of activists has been fished for some time," said Andy Card, of Vice President Bush's New Hampshire campaign. "The battle of the activists is almost over," said Paul Young, manager of the presidential campaign of Rep. Jack Kemp (R-N.Y.).

In this struggle for the party's elite, everyone acknowledges that Bush is the winner. And everyone agrees that such institutional backing provides no guarantee of victory. Bush's backers include Gov. John H. Sununu, Rep. Judd Gregg, over 80 state representatives, several sheriffs, state committee representatives and an assortment of others.

Kemp, in turn, has done far better in the preliminary stages than his standing in public polls suggests. He had put together a network of supporters second only to Bush's, according to operatives in most competing camps.

Kemp has lined up Sen. Gordon J. Humphrey, Rep. Robert C. Smith, about 40 state representatives and key leaders of the "right-to-life" and pro-gun forces. His opponents contend, however, that his organizational strength has failed to grow beyond a network of hard-core conservatives.

Sen. Robert J. Dole (R-Kan.), while claiming a willingness to "spot them {the Bush forces} the head table and we'll go after the audience," has been no slouch seeking a piece of the head table. He has acquired the backing of state House Speaker Doug Scammon, House Majority Leader Vincent Palumbo and former governor Walter Peterson and is expected to pull Sen. Warren B. Rudman into his camp.

At the same time, all the GOP presidential campaigns are nervously watching the political wild card of the 1988 primary, Marion G. (Pat) Robertson. The Christian talk-show host turned presidential candidate has in the main opted out of the endorsement wars but boasts that he will get at least 50,000 votes in the Feb. 16 primary -- enough to come in somewhere from first to third, if the claim proves true.

"We just don't know how to gauge the Robertson campaign. They are dealing with a different set of people than you usually deal with in a New Hampshire primary," a Bush strategist said.

Officials of the Robertson and Bush campaigns pointedly argue that the Kemp organization has been faltering after a strong start. "Everybody talks about Robertson: Can he reach out beyond his base?" said Robertson's Northeast political director, Kerry Moody. "But at least he's got a base. Kemp lined up the hard-core conservatives, the same group that supported {Rep.} Phil Crane {R-Ill.} in 1980, but he hasn't been able to go beyond that," he added in a comment repeated almost verbatim by Bush aides.

Joseph W. McQuaid, vice president and editor of the conservative Manchester Union-Leader, said, "I don't think Kemp has caught fire in New Hampshire or anyplace." He said Kemp claims to the contrary are "whistling in the graveyard."

Young, Kemp's New Hampshire manager, countered that Bush's supporters "are more the elitist, Republican country club set," and he argued that Dole's base of support has been restricted to the "liberal-moderate wing of the party." He said Robertson remains an unknown in the race but argued that Robertson's supporters will begin to "look at us as a viable candidate" to defeat the front-runner, Bush.

The Republican contest has advanced further than the Democratic one in the activist-courtship stage, in part because the GOP candidates are better known and in part because of the turbulence of the Democratic contest. As former senator Gary Hart and then Sen. Joseph R. Biden Jr. (D-Del.) withdrew, their impressive array of backers has been returned to the pool of available Democratic activists.

On the Republican side, major uncommitted figures include Nackey S. Loeb, Union Leader publisher, an important conservative voice in the state; former governor Meldrim Thompson, and key 1980 Reagan backer Gerald Carmen. Thompson and Carmen had backed former senator Paul Laxalt (Nev.) until he decided against running.

All three are encouraging former U.N. ambassador Jeane J. Kirkpatrick, who is appearing here today, to consider entering the presidential contest.

Running far behind in the endorsement contest are former Delaware governor Pierre S. (Pete) du Pont IV and former secretary of state Alexander M. Haig Jr. "I'm conceding that . . . , " said Fred Maas, du Pont's New Hampshire manager, "how can you compete with a guy like Bush, who in 1980 started organizing 10-year-olds?" He contended, however, that, "unlike Bush, Dole and Kemp, who are building a foundation, we are building a ditch. And into that ditch are falling disenchanted Bush, Dole and Kemp people."