Du Pont's Breakfast Topic: An 'Important Crossroad'

Former Delaware governor Pierre S. du Pont IV, a potential candidate for the 1988 Republican presidential nomination, has invited 200 friends and supporters for breakfast on June 3 at the Hotel Du Pont in Wilmington.

Du Pont, who has been traveling the political circuit -- including Iowa and New Hampshire -- for the last 18 months, wrote in a note attached to the invitation: "We are reaching an important crossroad. On June 3 I want to tell you about the directions in which we are heading."

The first hat in the presidential ring? "It is a general briefing for friends and supporters," du Pont political aide Glenn Kenton said. "There will be no announcement of any campaign for anything." New Hampshire Lawmakers Back Kemp

In New Hampshire, more than 100 Republican state legislators and local officials have written a letter to Rep. Jack Kemp (R-N.Y.) "urging" him to throw his hat into the presidential ring, beginning with the 1988 New Hampshire Republican primary, because "we believe you are the individual best suited to continue the Reagan revolution."

Roger Stone, a Kemp political adviser, said, these people "are the nucleus of a first-rate grass-roots organization . . . they are not the big shots, they are the people who will go out and hustle." Dole Reaches Out in New Hampshire

Senate Majority Leader Robert J. Dole (R-Kan.), another potential 1988 Republican presidential contender, may be looking to do some organizing in New Hampshire.

Donald J. Devine, chairman of Dole's political action committee, Campaign America, said that he has "had discussions" with Gerald Carmen about joining the Dole effort. Carmen, from New Hampshire, was responsible for running the winning 1980 Reagan campaign in that state. Nine Running for Governor in Maine

It must be a good job -- nine people want to be the next governor of Maine. Gov. Joseph E. Brennan (D), barred by law from a third term, is running for the House seat being vacated by Rep. John R. McKernan Jr. (R), who is running for governor. McKernan is favored to win his primary June 10 as is Attorney General James Tierney (D).

Looking to the general election race between these two and two independent candidates, a Democratic strategist predicts that "nuclear waste is an immense issue that would change the course of the election if one of the candidates could become identified with it."

The federal government had selected two locations in Maine as potential sites for a permanent nuclear waste dump, but announced yesterday that the search for a site in the Northeast had been indefinitely postponed. But many in Maine are not convinced the issue will go away, and Tierney pollster Tom Kiley contends that "the candidate who can convince the voters that he or she will be most effective in keeping the waste out of Maine will have the advantage." Raising Funds to Save Hill Staffers

Rep. Barney Frank (D-Mass.) decided he cannot afford to lose any of his staff, but he cannot afford to keep all of them under the cuts mandated by the Gramm-Rudman-Hollings deficit-reduction law.

So Frank has invited supporters to a fund-raiser June 9 to raise money for a fund to pay the salaries of congressional staffers turned campaign staffers. Frank, who is not being seriously challenged for reelection, said staffers will take leaves from his Hill office to work on campaign-related activities for him or for candidates "who represent the same views that I have and who are in difficult races."