Senator John McCain of Arizona, who is regarded as a dark horse who could take the nomination if George Bush Jnr falters, says that the party should return to its pre-1980 position, when it expressed opposition to abortion but acknowledged it as a question of conscience where there were differing views.
Mr McCain was throwing down the gauntlet to local party organisations, especially in the south, which have made absolute opposition to abortion a precondition for granting party funding to candidates for political office. The "pro-choice" stance of Christine Whitman, the Republican governor of New Jersey, severely limited her ability to solicit funds, and she was re-elected in 1997 by only the slimmest of margins.
The party caucuses have the determining voice in the selection of the presidential candidate, and for a generation a firm anti-abortion line has been the first hurdle for any aspiring candidate.
In 1996, the party went further, saying that unborn children "have a fundamental individual right to life which cannot be infringed".
Mr McCain's comments were the latest sign of a retreat from this position. The last presidential election showed a wide gender gap in the Republican vote, with many fewer women voting for Bob Dole than men, and abortion was seen as one factor. Both leading candidates for the Republican nomination - George Bush Jnr and Elizabeth Dole - have stayed away from committing themselves on the issue.
An alteration in the party's stance on abortion would be the first real evidence that the influence of the religious right was starting to wane. A precursor was the American public's response to the Monica Lewinsky affair, where attempts by the party to campaign on a strictly moralistic platform were a liability in last year's mid-term elections.