Hillary Clinton narrowly leads the pack of Democratic hopefuls in New Hampshire, with Barack Obama coming in a close second. In addition, while Bill Richardson is barely on the radar screen nationally, he receives double-digit support in the Granite State and comes in fourth behind John Edwards.

A FOX News poll of likely New Hampshire Democratic voters finds that Clinton has the support of 30 percent followed by Obama at 23 percent. Edwards comes in third with 17 percent, Richardson receives the support of 12 percent. All other candidates receive 3 percent or less.

Although Clinton has a slim advantage in the trial heat, slightly more Democratic primary voters say they would be very or somewhat satisfied if Obama (74 percent satisfied) were the party’s presidential nominee than if Clinton won (69 percent satisfied).

Click here to view the full results of the poll. (pdf)

"We seem to be seeing a softening in the Clinton vote everywhere," said Opinion Dynamics CEO John Gorman. "The inevitability of a month ago has been replaced by serious sound thoughts. What’s interesting is that this seems to be not a surge to second place Obama, but reexamination of candidates even farther down the list. Edwards is closer to Obama than Obama to Clinton and Richardson closer to Edwards than Edward to Obama. An Edwards second or a Richardson third might shake things up as much as a Hillary defeat."

Looking at the primary vote among some key groups, by a 33 percent to 24 percent margin, women favor Clinton over Obama. And married women are even more likely to back Clinton (38 percent to 24 percent).

Among men the results are more evenly divided, although Clinton still has the advantage: 26 percent say they would vote for Clinton, followed by Obama at 21 percent, Edwards at 18 percent and Richardson at 14 percent.

Voters with a college degree split almost evenly between Clinton (26 percent) and Obama (24 percent); voters without a college degree strongly back Clinton by a margin of 42 percent to 17 percent for Obama and 16 percent for Edwards.

Democratic primary voters in New Hampshire say the most important issue in deciding their vote is the candidate’s position on the Iraq war (36 percent), followed by health care (25 percent) and the economy (18 percent).

Voters who put Iraq and health care at the top of their list are slightly likely to support Clinton. Among economy voters, Clinton (41 percent) is the clear choice, as she outperforms Obama (27 percent) by a double-digit margin.

The poll finds that these New Hampshire Democratic voters are looking for the candidate who is the "most honest and trustworthy;" nearly one third of voters (32 percent) say this is the most important quality in deciding which candidate to support. The other top factors include having "the right experience" (22 percent), understanding "average Americans" (16 percent) and having "new ideas" (13 percent).

Both Obama (28 percent) and Edwards (24 percent) top Clinton (18 percent) among those looking to vote for the "most honest and trustworthy" candidate.

Obama has a significant advantage among voters who are looking for new ideas (51 percent to 17 percent for Clinton).

For voters who say they are looking for a candidate with the right experience, Clinton is the clear choice (55 percent) and Richardson comes in second (22 percent) followed by Obama in the single-digits (7 percent).

With less than 40 days until they go to the polls for New Hampshire’s January 8 primary, more than 4 in 10 Democrats say they are "extremely interested" in the election, and half say they have settled on the candidate they will support.

More Clinton voters are committed to their candidate than Obama voters are: A 70 percent majority of Clinton’s supporters say they are certain to vote for her, while 56 percent of Obama’s supporters say they are certain to back him.

The telephone poll was conducted for FOX News by Opinion Dynamics Corp. among 1,000 likely presidential primary voters in New Hampshire, including 500 likely Democratic primary voters, from Nov. 27 to Nov. 29. The entire poll has a 3-point error margin and a 4 point error for the subgroup of Democratic presidential primary voters.