The National Congressional Club, the powerful New Right political machine built by allies of Sen. Jesse Helms (R-N.C.), will be challenged on its home turf next year in the North Carolina Republican Senate primary by another influential conservative political action committee.

The Fund for a Conservative Majority (FCM) has decided to back Rep. James T. Broyhill (R-N.C.), the dean of the state's congressional delegation, in his effort to succeed Sen. John P. East (R-N.C.), who announced last week that he will not seek a second term because of ill health.

This sets FCM directly at odds with the Congressional Club, which has endorsed David Funderburk, a Campbell College government professor and former U.S. ambassador to Romania, and pledged to raise from $5 million to $10 million in his behalf.

In money terms, the FCM enforcement of Broyhill is far less valuable. According to FCM chairman Robert Heckman, the organization intends to donate $5,000 to Broyhill's primary campaign and help him raise additional funds from Washington-based conservative organizations.

But the battle has symbolic importance, pitting conservative pragmatists against ideologues. Funderburk, 41, is a political unknown who has never run for public office, just as was East, a former college professor, when he was elected with Congressional Club help in 1980. Broyhill, first elected to the House in 1962, is a pillar of the GOP moderate establishment.

Heckman said he is supporting Broyhill because he has a "much better chance of winning" and "passes our litmus tests for being a conservative."

"I don't think a political novice is going to win a general election," he added. "The fact is this isn't 1980. Ronald Reagan isn't on the ticket and you aren't going to sneak up on anyone in North Carolina." Colorado GOP Invites NCPAC Out

Republicans in Colorado, preparing for a 1986 Senate race that may or may not include Sen. Gary Hart (D-Colo.), have their problems, too. The chairman of the Colorado Republican Party is saying "thanks but no thanks" to a $250,000 campaign by the National Conservative Political Action Committee (NCPAC) to unseat Democrat Hart.

A group of Colorado Republican activists, calling themselves the "Gary Hart Truth Squad," plan to wage a NCPAC-financed advertising campaign to undermine Hart's chances for reelection.

"I can only say thanks but no thanks," said Howard H. (Bo) Callaway. "Colorado Republicans don't need outside groups to help them win elections. Maybe there are other states that can use that kind of help. If so, we urge NCPAC and all other outside groups to take their campaigns elsewhere."

Hart has not yet announced whether he will seek a third term in the Senate next year or give up his seat to focus on a second bid for the Democratic presidential nomination in 1988. Bush, Kemp Issue Clips to Media

A lesser element of a prospective presidential campaign is sending news clips to the media to show how much strong "play" is being given a candidate. Vice President Bush, for example, sent a large package last month, with a long magazine article detailing his World War II heroics firmly stapled atop the pile.

More recently, Rep. Jack Kemp (R-N.Y.) has added a new twist. In an apparent effort to show that his unannounced candidacy for the White House is taken seriously around the world, he sent newspaper clippings including coverage in English of his recent Far East trip and clippings from Japanese and Chinese newspapers. 'West Point' of U.S. Politics

Republican leaders yesterday announced plans to spend $1 million to finance 10-week campaign training sessions for 140 prospective managers, finance directors and public relations specialists.

Rep. Guy Vander Jagt (R-Mich.), chairman of the National Republican Congressional Committee, claimed that the Republican Congressional Campaign Academy, which pays "students" $300 a week to cover room and board, will become "the West Point of American politics."