If the Republicans are to become a permanent majority party, they have to expand their base.   Michael Barone has argued that the 2002 election might have been a way station to real Republican control (a six percentage point Congressional vote margin), but it needs to be confirmed a few times for it to be real. The 2002 election followed several virtual ties in both the national Congressional vote and of course the 2000 Presidential election.

Demographic trends are mixed. The rapidly growing Hispanic population favors the Democrats. The growth of the religious Christian community, whose birth rate greatly outnumbers that of the secular population, is a boon for the GOP (many surveys show young people are more conservative and supportive of the GOP, than the general population). The huge increases in the number of Americans with graduate degrees, appears to favor the Democrats (David Brooks' "bobos in their latte towns").

Were Rudy Giuiiani to slay the last standing Clinton, it is not so he can become a Senator, one of a 100.  Giuliani, unlike most Senators, has actually run something. In the 2002 election, he was the second most popular Republican on the stump, after the President.

When John McCain, a close friend of Giuliani, ran for President in 2000, he was too liberal for the Party, despite his allegiance to the mainstream anti—abortion views of the Party. If Giuliani were to get his Party's nomination, it would represent a sea change in politics. Bill Clinton's greatest success was attracting educated, wealthy, white suburbanites from the GOP to the Democrats, by easing their concerns that the Democrats were soft on crime, weak on defense, supportive of welfare over work, and most importantly, by portraying the GOP as a party of Southern anti—abortion bigots. 

This is why New Jersey, Illinois, Connecticut and other states have moved to the Democrats in the past ten years.

Giuliani would burst this bubble. His abortion views and attitudes on gays, would still seem today to be a big hurdle for many  GOP party regulars. But if Giuliani took down Hillary, he would end the fears of a second coming of the Clintons. That would be a very big deal for many Republicans, regardless of their social views. Were Rudy to win the nomination and then the White House in 2008, the GOP would suddenly seem a lot less scary party to its traditional affluent and educated suburban patrons.

Winning back the suburbs would indeed spell the death knell for the Democrats, a party currently moving full steam ahead towards national marginalization, on the backs of an internet frenzied anti—war Dean movement.

But parties recover. The GOP won the Presidency in 1968 ,after winning only 6 states with Goldwater in 1964. Clinton took the Democrats from three straight big defeats to two solid Presidential election wins, one over an incumbent. The Democrats can recover, and a centrist positioning by Hillary probably represents their best hope to do so in 2008, especially if Dean takes the party left, and down hard in 2004.

So a Giuliani defeat of Hillary in 2006 would be a significant event for the Republicans' future. That would leave Al Gore to compete against either Giuliani, Condi Rice, or Bill Frist in 2008.  A Giuliani—Rice ticket would in one swoop shatter two important pieces of the Democratic base: black voters, and socially liberal, well—educated suburbanites.