President Reagan will address a fund-raising luncheon in New York City for Sen. Alfonse M. D'Amato (R-N.Y.) on April 18. Cochairman of the event is none other than Chrysler Corp. Chairman Lee A. Iacocca, who was recently fired by the Reagan administration as chairman of the Statue of Liberty-Ellis Island Centennial Commission. Iacocca, who is sometimes mentioned as a potential Democratic presidential candidate, has said he is a Republican.

Democrats are fretting that D'Amato, who will have about $6 million in his campaign warchest by late April, still has no big-name opponent. There were rumors last week that former mayor John V. Lindsay or Rep. Stephen J. Solarz might run against him, but both denied having any interest. However, Mark Green, public interest lawyer and former congressional candidate, says he'll run no matter what big gun might be trotted out. Ins:

* Once again, Orval? Former Arkansas governor Orval E. Faubus (D), whose use of National Guard troops to prevent school desegregation 30 years ago made him a nationally known figure, is running for the Democratic gubernatorial nomination again. Faubus, 76, served six terms as governor -- an Arkansas record -- from 1954 to 1966, then ran unsuccessfully in 1970 and 1974. He lost the first time to Dale Bumpers, now the state's senior senator, and in 1974 to David H. Pryor, the junior senator. Faubus and black activist Robert McIntosh are challenging Gov. Bill Clinton (D), who has served three two-year terms. Outs:

* Millionaire Herbert Kohl, who many Wisconsin Republicans and Democrats thought would be the most serious challenger to Sen. Robert W. Kasten (R), decided not to enter the race for the Democratic Senate nomination. Kohl had hired polling and media consultants, but in the end, according to a Democratic official, "the consultants were willing, but the candidate was not."

Kohl is the eighth Democrat to decline. The others were Gov. Tony Earl, House Speaker Thomas Loftus, Senate Majority Leader Tim Cullen, Attorney General Bronson LaFollette and Reps. Les Aspin, David R. Obey and Jim Moody.

Fighting it out for the nomination are former state party chairman Matthew Flynn and Ed Garvey, former executive director of the National Football League Players Association.

Massachusetts State Reps. Thomas J. Vallely and William F. Galvin have withdrawn from the race for the Democratic nomination for the House seat of Speaker Thomas P. (Tip) O'Neill Jr., who is retiring. There are still 10 Democrats in the race. Polls show Joseph P. Kennedy II with a 2-to-1 lead over his nearest rival. Earlies:

* South Dakota, which used to hold its presidential primary in June, on the last Tuesday of the primary season, is now the second primary state after New Hampshire. Gov. William J. Janklow (R), after first saying he would veto it, signed a bill changing the date to the last Tuesday in February, expressing hope that the early primary campaign would attract more attention to farm problems. This puts South Dakota's primary, like New Hampshire's and the Iowa caucuses, ahead of the national Democratic Party's recommended primary period of early March to early June. Polls

* Two new polls on the Florida Senate race show Gov. Robert Graham (D) with a narrow lead over incumbent Paula Hawkins (R). One taken March 4-9 by Hawkins pollster Dick Morris puts Graham ahead 44 to 40 percent. A poll taken at about the same time by The Miami Herald shows him leading 49 to 40 percent. These polls contrast with one taken last month by Graham pollster Bill Hamilton, which gave Graham a 17-point lead.

Vice President Bush was the first choice of 38 percent of the Republicans polled a year ago in a Harris Survey of potential 1988 presidential contenders. The latest survey shows him the first choice of 29 percent, followed by former Senate majority leader Howard H. Baker Jr. (Tenn.) with 16 percent, Senate Majority Leader Robert J. Dole (Kan.) with 15 percent, former secretary of state Alexander M. Haig with 8 percent and Rep. Jack Kemp (N.Y.) and former U.N. ambassador Jeane J. Kirkpatrick with 6 percent each. Evangelical preacher Pat Robertson received 3 percent.

The same poll shows Sen. Gary Hart (D-Colo.) as the frontrunner in the 1988 general election, leading Bush 54 to 43 percent. A year ago, Hart and Bush were tied at 48 percent. When matched against Kemp, Hart leads by 65 to 30 percent.