Major boost for Nikki Haley as she far surpasses Ron DeSantis for second place in New Hampshire - trailing Trump by only 15% in a poll just 37 days before the primary election

Donald Trump still has a head start in New Hampshire, but his lead is shrinking with a new poll showing Nikki Haley closing the gap with the ex-president while also overtaking Florida Gov. Ron DeSantis for second place.

The former United Nations Ambassador is not only ahead of DeSantis by 18 points in New Hampshire, but she is also only trailing Trump by 15 percent, according to a new CBS News/YouGov poll released on Sunday.

Twenty-nine percent of likely Republican primary voters in the Granite State prefer Haley, with 55 percent of the electorate describing her as 'likable' compared to 37 percent who say the same about DeSantis and 36 percent who say that about Trump.

DeSantis is only 1 percentage point ahead of former New Jersey Gov. Chris Christie, who as the only anti-Trump candidate remaining has focused all of his attention on clinching the New England state and has not yet stepped foot in Iowa for his campaign.

Trump has remained in first place in every national and state-wide poll in the Republican presidential primary race despite refusing to participate in the debates. And the numbers released on Sunday show that there's still a chance for other candidates to close the gap before the Iowa caucuses kick-off the primary contests on January 15.

New Hampshrie holds the second primary contest with its elections on January 23 – and the more liberal New England state is showing a leaning away from Trump.

In Iowa, Trump still leads the field of likely caucus-goers with 58 percent support, followed by DeSantis with 22 percent and Haley in third place with 13 percent, the CBS poll conducted December 8-15 shows.

The survey took a sampling of 1,054 registered voters in Iowa and 85 in New Hampshire.

Several previous Iowa polls have shown DeSantis and Haley tying for second place, but that latest shows a boost in the Hawkeye state for the Florida governor, who is ahead by 9 percent.

DeSantis received some boosts in Iowa by earning key endorsements from the likes of Gov. Kim Reynolds and evangelical leader Bob Vander Plaats. He also completed the 'full Grassley,' meaning he visited every single Iowa country before caucus day.

This has likely kept him in a solid second place for the majority of the primary contest so far.

Moving over to New Hampshire, Trump's first place lead significantly shrinks with only 44 percent support in the Granite State, compared to Haley's 29 percent and DeSantis' mere 11 percent.

DeSantis has seen a major drop-off in New Hampshire polls throughout the primary election season, most likely due to the fact many Republican New Hampshire voters are not as socially conservative as the Florida governor.

Haley – who has expressed more moderate social views, including on abortion – was able to overtake DeSantis in New Hampshire. The former South Carolina governor has also made significant headway with those who described themselves as more moderate or independent.

Biotech entrepreneur Vivek Ramaswamy had some early boosts in Iowa and New Hampshire, but has fallen off following some controversial positions and personal attacks levied at two separate debates in Miami, Florida and Tuscaloosa, Alabama.

In Iowa, Ramaswamy is in fourth place with 4 percent and in New Hampshire in fifth place with 5 percent.

Former Arkansas Gov. Asa Hutchinson, who has not made the debate stage since the first showdown in Milwaukee, Wisconsin, is earning around 1 percent or less in the early primary states.