Just last year, I saw him passionately deliver remarks at the Manhattan Institute Hamilton Award Dinner in which he condemned the “punitive approach” to immigration, “which is reflected in the House legislation that was passed, which is to make it a crime to be an illegal or undocumented immigrant.”

To “deal with it in a punitive way,” he said then, “is actually going to make us considerably less secure than we already are.” The better approach, he continued, is to embrace the Senate’s comprehensive reform and to separate the criminal illegals from the hard-working ones.

These speeches are the real Rudy. These speeches represent the Rudy who once went overboard and declared, “If you come here and you work hard and you happen to be in an undocumented status, you’re one of the people who we want in this city.”

This is why Fred Siegel, a Giuliani biographer, accurately called him an “immoderate centrist.” This is why Giuliani won 43 percent of the Hispanic vote in the mayoral race of 1997. This is why his candidacy once had the potential to renovate the G.O.P.

Of course it hasn’t turned out that way. At the moment, Giuliani and fellow moderate Mitt Romney are attacking each other for being insufficiently Tancredo-esque. They are not renouncing the policies they championed as city and state officials, but the emphasis as they run for federal office is all in the other direction. In effect, they are competing to drive away Hispanic votes and make the party unelectable in New Mexico, Arizona, Colorado, Nevada, Florida and the nation at large.

In this way, they are participating in the greatest blown opportunity in recent political history. At its current nadir, the G.O.P. had been blessed with five heterodox presidential candidates who had the potential to modernize the party on a variety of fronts. They could be competing to do that, but instead they are competing to appeal to the narrowest slice of the old guard and flatter the most rigid orthodoxies of the Beltway interest groups. Giuliani could have opened the party to the armies of dynamism — the sort of hard-working strivers who live in Brooklyn, Queens and the Bronx; instead he has shelved one of his core convictions.

Someday Rudy Giuliani will look back on this moment and wonder why he didn’t run as himself.