Updated

More voters see Hillary Clinton and Rudy Giuliani as "very likely" to win the presidency, if nominated by their respective parties, than think the same of other top tier candidates, according to a new FOX News poll. In addition, soon-to-announce candidate Fred Thompson improves his position in the Republican nomination race. Thompson’s current double-digit support puts him in third place — edging out Mitt Romney and on the heels of John McCain.

Opinion Dynamics Corp. conducted the national telephone poll of 900 registered voters for FOX News from June 5 to June 6. The poll has a 3-point error margin.

Compared to the other front-runners — Democrat and Republican — Hillary Clinton is seen by more voters as "very likely" to win the 2008 election. With the "if nominated" caveat, 35 percent of voters think it is very likely Clinton could win the presidency, while 29 percent think it is very likely Giuliani could be elected and 23 percent think the same of Obama.

If McCain were nominated, 15 percent think it is very likely he could win; 13 percent think so of John Edwards and 6 percent believe the same about Romney.

• Click here to see full results of the poll.

Despite Clinton having the largest percentage of voters who consider her electable, she receives the lowest ratings among the front-runners tested on being likeable, and honest and trustworthy.

Fully 76 percent of voters think Obama is likeable, 74 percent Giuliani, 64 percent think McCain is likeable and 56 percent Clinton.

The candidates are on more equal footing when looking at how their own party faithful feels about them. Among Democrats, 85 percent think Clinton is likeable and 83 percent Obama. For Republicans, 86 percent say Giuliani is likeable and 76 percent McCain.

Overall, on the trait of being honest and trustworthy, McCain has a slight edge with 59 percent of voters saying he is honest and trustworthy, followed closely by Giuliani at 58 percent, and Obama at 57 percent. At 47 percent, Clinton is the only candidate with less than half of voters saying she is honest and trustworthy, which is largely due to three-quarters of Republicans disagreeing.

"Perceptions of Hillary Clinton are an interesting study in contrasts," according to Opinion Dynamics Vice President Lawrence Shiman. "While voters hold relatively similar views of the personal characteristics of most of the top-tier candidates, her numbers stand out on most questions."

A clear 71 percent majority of voters sees Giuliani as a strong leader and 60 percent view Clinton that way; 59 percent see McCain as a strong leader and 49 percent Obama.

Presidential Primaries

In the race for the nominations, there is little change on the Democratic side this month, while there has been some movement among the Republican hopefuls. Giuliani continues to have the advantage with 22 percent, McCain holds onto his second place slot with 15 percent, though Fred Thompson is close behind at 13 percent, which puts him just ahead of Romney at 10 percent.

When Thompson voters are asked who their second choice would be, about a third opt for Giuliani and another third choose Romney, while a few are split between Gingrich and McCain. While it seems fair to say Thompson’s entry into the race hurts multiple candidates, right now he appears to take more votes away from Giuliani and Romney.

In the Democratic contest, 36 percent support Clinton (down just 1 point from last month), and 23 percent back Obama (up 3 percentage points). In the next tier there is former Vice President Al Gore at 14 percent and Edwards at 12 percent; no other candidates receive double-digit support.

If Gore is taken out of the mix, the top candidates each gain a few points, but the lineup stays the same with Clinton and Obama well ahead of Edwards.

One additional point on the primary vote — there are many more undecided voters on the Republican side, with 19 percent saying they are unsure compared to 9 percent of Democrats.

Head-to-Head Matchups

If the general election were held today, Giuliani would edge out both of the top Democrats —besting Clinton by 3 points (45 percent to 42 percent) and Obama by 5 points (46 percent to 41 percent).

Clinton has a clear advantage over lesser-known Republicans. For example, Clinton tops both Romney (46 percent to 36 percent) and Fred Thompson (48 percent to 38 percent) by 10 points. Between Clinton and McCain, it’s a tie: 43 percent each.

The poll also tested a three-way race with New York City Mayor Michael Bloomberg running as an independent against the two major party candidate front-runners. In that race Clinton receives 39 percent to Giuliani’s 41 percent and Bloomberg garners 7 percent.

If Clinton won the presidency, twice as many voters think her victory would be seen as electing the first woman to the White House (52 percent) rather than as another term for the Clintons (29 percent). Most Democrats (71 percent) would see it as the first woman president while a plurality of Republicans (45 percent) would see it as another Clinton term.

Furthermore, if Clinton were to win, slightly more voters (38 percent) say they would be "worried" about her husband Bill being back in the White House than "enthusiastic" (36 percent), while a 66 percent majority thinks he would avoid behavior that may get him into trouble.

Edwards was in the news recently for paying $400 for a haircut. Are voters paying attention? Overall, more than four of 10 voters (44 percent) are able to identify Edwards (in an unaided question) as the candidate with the high-priced hairdo; only 4 percent name any of the other candidates.

Job Ratings

Voters continue to be displeased with Washington, as majorities disapprove of the job President Bush is doing (57 percent) and the job Congress is doing (55 percent). The president’s current approval rating remains unchanged at 34 percent.