Just as America’s Republican Party is desperately searching for a more marketable identity, comes a reminder of its conflicted legacy: Jack Kemp, one of its most significant figures of the last thirty years, died of cancer at the weekend, aged 73.

Kemp first became famous as a professional gridiron player, but he turned to politics in the 1960s, working briefly for the then governor of California, Ronald Reagan. In 1970 he won a seat in Congress, which he held for 18 years, during which time he rose to prominence as the leading advocate of tax cuts. A modified version of his plan was enacted in 1981 when Reagan became president and is widely credited with fueling the economic boom of the 1980s.

Although he tried to position himself as Reagan’s heir, Kemp’s campaign for the presidency in 1988 never got much traction and he ended by endorsing George Bush Sr. Bush in turn appointed Kemp as secretary for Housing and Urban Development, but the two were never close and Kemp’s influence in the administration was seen as minimal.

After the failure of the first Bush presidency, the Republican Party went through a period of soul-searching similar to today’s. All sides revered Reagan and wanted to duplicate his success, but had differing interpretations of what that involved. As the decade progressed, more and more of the optimistic, pro-growth side of the Reagan persona was appropriated by Democrat Bill Clinton; the GOP became more the prisoner of the narrow, “movement” conservatism that led to George Bush Jr and Dick Cheney.

Many conservatives supported Kemp, but he never really fitted their model. Like Reagan (and Barry Goldwater before him), Kemp had little time for the religious fundamentalists; although he was anti-choice, he was generally moderate on social issues and a strong supporter of immigration and civil rights. Kemp consistently pushed programs to fight poverty and reach out to African Americans and other minorities.

Whereas some of the supply-siders (including tax cut guru Arthur Laffer) supported Clinton and later Barack Obama, Kemp stayed loyal to the GOP. In 1996 he ran as vice-presidential candidate with Bob Dole, in an “odd couple” ticket that failed to dent Clinton’s majority. He never sought office again, but remained politically active and endorsed John McCain in last year’s election.

Despite his own lack of success, Kemp in a sense represented what the Republicans are now looking for: a small-government position that doesn’t frighten conservatives, but is upbeat and inclusive in outlook. The problem they face is that so much of that territory — including the admiration for Reagan — has been occupied by Obama, leaving the GOP with the fundamentalists, the racists and the supporters of torture.

They’re not really Jack Kemp’s crowd.