LOS ANGELES, May 2 — As they gather Thursday night at the Ronald Reagan Presidential Library for their first debate, the Republican presidential candidates are thrilled at the chance to associate themselves with Reagan. But they may not be able to escape the challenge created for them by the current president.

As much as Iraq or health care or any other issue, the question of how to deal with President Bush is vexing the Republican field. Do they embrace him as a means of appealing to the conservative voters who tend to decide Republican primaries? Or do they break from him in an effort to show that they will lead the nation in a new direction? Do they applaud his policies or question his competence — or both?

Already, the leading candidates are showing clear divisions on that score. In formally announcing his candidacy last week, Senator John McCain of Arizona, without naming Mr. Bush, attacked the performance of the White House at home and abroad. In doing so, he separated himself from his two main rivals, Rudolph W. Giuliani and Mitt Romney, who have chosen to stick close to Mr. Bush, or at least to avoid breaking openly with him.

Aides to the candidates, who spent Wednesday in Southern California preparing for the debate, said they expected Mr. Bush and his record to be present in spirit when they began taking questions. Mr. McCain’s advisers said their candidate, who spent the day at his condominium in Coronado, expected — and welcomed — an opportunity to expand on his differences with the White House.