If Giuliani runs as a third party (Liberal Party for example, since he still hasn't declared as a Republican) and Nader runs again, the Democrat vote among liberals might be split beyond any hope of winning. That would leave an open door for a conservative GOP candidate.
All of the Giuliani supporters are assuming he will be the GOP nominee. Not unless he enters the GOP primaries as a Republican. So far, he hasn't.
And FYI...the Liberal Party of New York doesn't run it's own candidate; neither has the Conservative Party of new York.