Senator Hillary Clinton’s lead in the first-in-the-nation New Hampshire Primary has fallen to its lowest level of the season.

The latest Rasmussen Reports telephone poll of the state’s Likely Primary Voters shows Clinton leading Senator Barack Obama by ten percentage points, 34% to 24%. Former Senator John Edwards attracts 15% of the vote while New Mexico Governor Bill Richardson earns 8%. No other candidate tops the 3% level of support. (see crosstabs)

At 34%, Clinton’s current level of support is the lowest measured in any Rasmussen Reports poll this year. Four previous polls in New Hampshire found her consistently in the 37% to 40% range.

This is the first poll of the race conducted since Senator Hillary Clinton’s debate gaffe concerning drivers licenses for illegal immigrants. In the last poll before that debate, Clinton held a sixteen-point advantage over Obama. A month earlier, Clinton was ahead by twenty-three percentage points.

The current poll also shows that Clinton’s favorability ratings have dropped. Among New Hampshire’s Likely Voters, 72% now offer a positive assessment of the frontrunner. That’s down from 81% prior to the debate. Obama is viewed favorably by 82%, Edwards by 76%.

As in earlier surveys, Clinton continues to benefit from a substantial gender gap. She is tied with Obama among male voters but has a seventeen point advantage among women. Forty percent (40%) of women have a Very Favorable opinion of Clinton while only 8% have a Very Unfavorable view.

The results are far different among men—22% Very Favorable and 16% Very Unfavorable. A recent analysis of national survey results found that Clinton might attract a sizable number of Republican women while losing Democratic men to the GOP candidate.

Just 19% of Democratic Primary Voters in New Hampshire believe that drivers licenses should be made available to undocumented workers. Sixty-six percent (66%) disagree. A separate survey released yesterday found that Democrats nationwide hold similar views with 68% opposing the policy.

Fifty-one percent (51%) of Democratic Primary voters believe that when police pull someone over for a traffic violation, they should automatically check to see if the driver is in the country illegally. Thirty-eight percent (38%) believe that illegal immigrants discovered in this manner should be deported while 31% disagree. Half (51%) believe that such a policy invites discrimination.

Following Clinton’s debate gaffe, Rasmussen Reports national polling detected no immediate decline in support for the frontrunner. However, her numbers in the daily Presidential Tracking Poll have softened somewhat in the past few days.

Still, while the latest numbers show some movement, it’s important to note that Senator Clinton retains a double digit lead both in New Hampshire and nationally. Also, Clinton’s support is more solid than that of her challengers. Fifty-five percent (55%) of Clinton supporters in New Hampshire say they are certain they will vote for her. Just 43% say the same about Obama while 33% of Edwards’ voters are that certain.

Crosstabs are available to Premium Members only.