In polls taken in June and July by Zogby, Rasmussen and Newsweek , Edwards beats Fred Thompson by an average of 11%, beats Mitt Romney by an average of 12.4%, beats John McCain by an average of 7.3%, and beats Rudolph Giuliani by an average of 2% (which is still greater than Hillary's match-up with Giuliani which puts her ahead by 1%). Only Barack Obama comes out with a higher average margin of victory against Giuliani (3.2%), Thompson (13%) and Romney (13%). There is a summary of the polls on RealClearPolitics.
However, in the most recent Rasmussen report, Edwards has a 7-point lead over Giuliani, up from a 4-point lead in early June. Also, Rasmussen says that Republican voters are less opposed to Edwards than to Clinton or Obama. Giuliani and Thompson only get 68% of the Republican vote when pitted against Edwards.
Giuliani said recently that he was a "first responder" on 9/11 and that he was at Ground Zero "as much or more than" the workers who were digging through the rubble. Rudy will continue to draw as many connections as he can between himself and the events of that day. But many fire departments have complained that it was the Giuliani administration that short-changed them and made them lack necessary equipment that could have saved lives. Giuliani's comments - not to mention his lack of humility - show an insensitivity.
And Mitt Romney, when asked why none of his five sons were serving in the military, said that his sons were serving their country by trying to get him elected because "they think I will be a great president." No doubt there are thousands of Americans serving in Iraq who would rather work on a destined-to-fail political campaign instead of fighting in a war. Romney certainly can challenge Giuliani in the lack of sensitivity department.
Meanwhile, the Edwards campaign has been addressing matters of substance and talking specifics while the Republicans are beating their chests and making ill-considered quips. Edwards' health care plan remains the most thorough of those presented by any candidate (only Obama also has a substantive plan on the table). As pointed out earlier, Edwards has been setting the agenda for the Democratic contest by addressing issues and concerns that the other candidates must comment on.
UPDATE: Although not widely reported, Edwards won a California straw poll held in Los Angeles over the weekend by the California Democratic Council. The CDC is made up of Democratic clubs and organizations throughout the state. Edwards got 41% of the vote, while 20% were undecided. Obama placed next with 14%. Clinton received 8% of the vote.
More info: The Real Liberal