Could it be Clinton versus Giuliani in 2008? If the two major political parties were selecting their nominees today, New York Sen. Hillary Clinton (search) would be the choice for Democrats and former New York City Mayor Rudy Giuliani (search) for the Republicans.

In the latest FOX News poll, Clinton trounces the competition and receives the backing of 44 percent of self-described Democrats. Familiar names — the party’s 2004 ticket — follow her: Massachusetts Sen. John Kerry (search) receives 17 percent and former North Carolina Sen. John Edwards 14 percent.

Among self-described Republicans, Giuliani (29 percent) edges out Arizona Sen. John McCain (search) (26 percent). No others receive double-digit support, but former House Speaker Newt Gingrich is closest at 9 percent.

Opinion Dynamics Corporation conducted the national telephone poll of 900 registered voters for FOX News on June 14-15.

Most voters think it is likely that a woman will be on one of the presidential tickets in 2008, either as a presidential or vice presidential candidate. Over three-quarters think it is likely and more than 4 in 10 think it is "very likely" (44 percent). Hedging their bets, women (75 percent) are slightly less likely than men (81 percent) to think it is likely a female will be on a 2008 ticket.

The poll asked a handful of questions pairing two prominent women in Washington: Sen. Clinton and Secretary of State Condoleezza Rice. By 49 percent to 35 percent, Clinton is seen as "tougher." Rice has a slight advantage on "smarter" (38 percent Rice, 36 percent Clinton).

Equal numbers (54 percent each) think Clinton and Rice have the integrity to serve as president. It is widely believed that Sen. Clinton will enter the race; while Rice is arguably the most prominent Republican woman today, she has said she has no desire to run for president.

For fun, the poll asked voters how they would view a Hillary Rodham Clinton presidency — would it be her presidency or would it really be a third term for Bill Clinton? A sizeable majority (67 percent) would see it more as her term in office, with about one in five (19 percent) calling it a "third term" for the former president.

"It is clear that unlike some political spouses who are seen as merely extensions of the officeholder, Hillary Clinton is viewed as an independent and credible political figure in her own right," comments Opinion Dynamics President John Gorman. "Of course, this also means that she has made her own set of political enemies and critics. Even before President Clinton was elected, she was far more visible and more controversial than any other presidential spouse at least since Eleanor Roosevelt."

And how do voters feel about the possibility of former President Clinton being back into the White House? As in many things these days, opinion is divided: 38 percent say "enthusiastic" and 33 percent "scared."

Howard Dean in the News

Recently former Vermont Gov. Howard Dean has been in the news in his role as chair of the Democratic National Committee. Dean has made several remarks, such as suggesting that Republicans are untrustworthy, that caught the attention of not only Republican leaders, but also several in his own party as well.

Overall, about 4 in 10 voters say they are familiar with Dean’s recent comments, 21 percent say they are "very" and 20 percent "somewhat" familiar. Of those familiar with his remarks, few (27 percent) think Dean was speaking for most Democrats (62 percent say he was not).

Dean’s favorable rating has dropped 10 percentage points since earlier this year. Currently 23 percent of voters have a favorable view of Dean, down from 33 percent in March, and 41 percent have an unfavorable view. And even though Dean ran for president in 2004, many voters are either unable to form an opinion (24 percent) or have never heard of Dean (13 percent).

Just over half of voters (52 percent) have a favorable opinion of Hillary Clinton and about a third unfavorable (37 percent).

Likewise, President George W. Bush’s favorable rating is 52 percent, with 42 percent unfavorable.

2004 Vote for President: Few Want a Mulligan

An overwhelming majority of voters say they still agree with their vote choice in the 2004 presidential election. Fully 92 percent say they would stick with their guy. Only 3 percent say they regret their vote and another 2 percent have mixed feelings.

Virtually all of Bush and Kerry voters (94 percent) still agree with their vote. Four percent of Bush voters say they regret how they voted, as do 3 percent of Kerry voters.

Even though it was recently reported that Bush had slightly higher grades than Kerry did at Yale University, a 43 percent plurality of voters still think Kerry is the one with better grades. About a quarter (27 percent) got it right and say Bush had better grades in college.

• PDF: Click here for full poll results.