Two cabinet secretaries under consideration to be chairman of the Republican National Committee have signaled the White House their lack of interest in a job that is showing signs of changing from a plum to a sour grape.

Aides to Transportation Secretary Samuel K. Skinner and Commerce Secretary Robert A. Mosbacher said the two have told White House officials that they do not want the party chairmanship, which former drug policy director William J. Bennett turned down this week over money.

The job has been accumulating liabilities, including hostility from the right, a dearth of funds and a role of subservience to the White House and its staff.

President Bush and his chosen GOP chairman could be challenged by the Republican right. "What conservatives are going to do is try to get {President} Bush back in line or get rid of him," said Burton Yale Pines, senior vice president of the Heritage Foundation.

Paul Weyrich, head of the Free Congress Foundation, said the Bush administration "has lost credibility because the tax pledge was of enormous importance," referring to Bush's abandonment of his promise not to raise taxes.

At the same time, contributions to the Republican National Committee, the lifeblood of the party, have been declining sharply. The 1989-90 election cycle was the worst of the last four election cycles for the RNC in terms of campaign receipts. From a high of $97.6 million in receipts in 1983-84, income fell to $75.6 million in 1985-86, rose slightly to $82.8 million in the 1987-88 presidential cycle, and collapsed to $60.8 million in 1989-90, according to the Federal Election Commission.

The new RNC chairman will succeed Bush's 1988 campaign manager, Lee Atwater, who is being treated for a brain tumor. Atwater's successor will need to be willing to take a role in the political pecking order subordinate both to the White House staff and to those selected to run Bush's reelection bid, according to GOP strategists.

"Whoever thinks this job has high visibility as a political policy-maker better think twice. It's a job for a loyalist willing to work in the trenches," said one GOP expert in national committee politics who asked not to be identified.

Furthermore, an ambitious politician seeking to use the RNC chairmanship to develop a reputation as a party builder could find Bush a liability. Bush has carried few fellow Republicans into office. Instead of his 1988 victory producing a coattail effect, the opposite was true: In battles for state legislative seats, Democrats gained in 1988 -- in contrast to strong GOP gains in both of Ronald Reagan's presidential elections. In 1988, Republicans lost three seats in the House, the first time since 1960 that the party winning the presidency lost House seats.

Charles R. Black, RNC spokesman, said the party chairmanship should be very attractive now. "For anyone looking at making a difference in terms of picking up {House} seats and expanding the party base, 1992 is the best opportunity since 1980," when the GOP picked up 34 House seats.

Sources said Bush took with him this weekend to Camp David a list prepared by White House Chief of Staff John H. Sununu of possible chairmen that included Richard Bond, former RNC deputy chairman and deputy manager of Bush's 1988 campaign; Attorney General Dick Thornburgh; outgoing New Mexico Gov. Garrey Carruthers; outgoing Sen. William L. Armstrong (Colo.); outgoing California Gov. George Deukmejian and former representative Tom Loeffler (Tex.).

Other possible candidates include Haley Barbour, a former Mississippi GOP official who is now a member of the RNC; outgoing Illinois Gov. James R. Thompson and former New Jersey governor Thomas H. Kean.

One GOP source said yesterday that party officials nationwide were frantically calling the RNC and White House about what this official called the "Bennett fiasco," referring to Bennett's abrupt decision to reject the post because it placed limitations on his outside earning.

"They are not happy out there and for good reason," the GOP source said. "The party has money problems, message problems and now we {have} a non-chairman chairman."