CONCORD, N.H. -- Three months before the New Hampshire primary, there are few signs of a serious conservative challenge here to Vice President Bush, the front-runner for the 1988 GOP presidential nomination, and his main rival, Senate Minority Leader Robert J. Dole (Kan.).

Public opinion polls and the impressions of Republican campaign aides and state party officials all suggest that Rep. Jack Kemp (R-N.Y.), who hopes to become the "spiritual heir" to President Reagan among Republican conservatives, remains stalled and has not expanded his hard-core base.

The other candidates -- former Delaware governor Pierre S. (Pete) du Pont IV, former secretary of state Alexander M. Haig Jr. and former television evangelist Marion G. (Pat) Robertson -- appear to have even less support, although Robertson's potential strength here remains a mystery.

Robertson has a smaller Christian evangelical base in New Hampshire than in Iowa, but he is running an aggressive, grass-roots campaign that is aimed at overtaking Kemp and finishing a respectable third to Bush and Dole. His strength is virtually impossible to measure because his supporters are generally not part of the partisan process and voters he appeals to may be registered Democrats or not yet registered at all, so they don't show up in opinion polls or talks with party leaders.

All of these second-tier candidates see the campaign in roughly the same way: That the Feb. 16 New Hampshire primary will provide the springboard for one of them to emerge as the authentic "conservative alternative" to Bush or Dole. As the leading public advocate of supply-side economics who long ago targeted New Hampshire as the key to his campaign, Kemp, in particular, appeared well positioned to make this strategy work.

But while Kemp has spent more time in New Hampshire than any Republican candidate except du Pont, there is little evidence that he is having much impact. A new poll of registered Republicans and independents that was released this week shows Bush with 50 percent, Dole second with 22 percent and Kemp a distant third with 7 percent.

While Bush and Dole continue to show modest gains, moving in tandem, this was the same level of support that Kemp had in January and May in polls by the University of New Hampshire and WMUR-TV in Manchester.

Asked in the most recent poll to name their top three choices for the GOP nomination, only one-quarter of the respondents included Kemp, while 71 percent named Bush and 53 percent Dole.

A September poll conducted for Sen. Warren B. Rudman (R-N.H.), a Dole supporter, showed Bush leading Dole, 37 to 22 percent. Kemp was again a distant third with 9 percent.

These preliminary findings may prove to be a poor guide to the outcome of the primary, but the apparent lack of movement by Kemp and the others is calling into question the underlying theory that large numbers of New Hampshire Republicans will find Bush and Dole unacceptably moderate and will search for an alternative.

Thomas D. Rath, a former New Hampshire attorney general and a key Dole operative here, said the party's conservative center has expanded during the Reagan years and that Bush and Dole are well within the consensus views of this enlarged base.

"Kemp is running an ideological race in which there is a great deal of ideological parity," he said. "It's very hard to say Bob Dole is not sufficiently conservative."

State GOP Chairman Elsie Vartanian said Kemp appeared to have been boosted by his Houston debate performance but that until then "I hadn't sensed any great momentum." She said she thinks that conservatives "are beginning to drift to Bush and Dole."

One notable exception to this trend is among New Hampshire's most conservative Republican forces, including the Manchester Union Leader, the only statewide newspaper, and former governor Meldrim Thomson Jr. But the influence of the newspaper and Thomson's cadre of followers is being increasingly questioned.

In his front-page column in the Union Leader this week, Thomson not only attacked Bush -- his favorite target -- but also Kemp. Accusing Kemp operatives of discouraging former ambassador to the United Nations Jeane J. Kirkpatrick from entering the race, Thomson declared, "In this campaign, I shall not march to the Kemp drumbeat."

Paul Young, Kemp's New Hampshire campaign director, professes unconcern about suggestions that the New Hampshire contest is gradually turning into a two-man race between Bush and Dole. "Polls mean nothing at this point. Polls mean name identification," he said.

According to Young, the Kemp organization won the invisible battle here to enlist conservative political activists over the summer and that will be translated into growing support as Kemp becomes better known. Like Kerry Moody, a former Kemp supporter who is now running Robertson's campaign in the Northeast, Young is counting heavily on Dole defeating Bush in Iowa, setting up a real test of the "conservative alternative" theory here.

"It's just a matter of time before Bush screws up," Young said. "If we are competing against Bob Dole in New Hampshire, there is no doubt we beat him. If Bush is wounded, the voters are going to look for an alternative between Bob Dole and Jack Kemp and more are going to vote for Kemp."