Handing out a press release that says you 'support' a candidate from your party is one thing - every politician does it - but a very visible Democrat Senator like Hillary Clinton going across the country into the candidate's state to personally make speeches and raise money for him is another, and quite notable. Her 'prestige' is on the line here, to a point. Davis loses big and it reflects on Hillary's vote-getting prowess - and her position in the Democrat party as well as with the general public.
Rudy Giuliani already has tons of prestige and power within his party and can easily expend some on Simon, if he chooses, which he will. If Giuliani can turn away whatever help Hillary Clinton gives to Davis and Simon surges ahead after a Giuliani visit or two, Rudy emerges even more powerful and Hillary is much diminished, if not with her party (they won't abandon her) then with the public, or at least the politically astute types that follow these things. That would be most of FR's members.