(CNN) Vermont Sen. Bernie Sanders heads into the New Hampshire primary still holding a lead over his top rivals for the Democratic nomination, but with Pete Buttigieg swiftly gaining support behind him, according to a new CNN poll conducted by the University of New Hampshire Survey Center.

All told, the near-even outcome from Iowa's caucuses appears to have given Buttigieg a bigger boost than Sanders. Overall, 28% of likely Democratic primary voters in New Hampshire back Sanders, about even with the 25% who backed him in mid-January. Buttigieg, the former mayor of South Bend, Indiana, has seen his numbers rise six points to 21%, while former Vice President Joe Biden slides five points to 11% and Massachusetts Sen. Elizabeth Warren dips to single digits with 9%.

Behind these top four, the poll finds no real movement in support for Hawaii Rep. Tulsi Gabbard (6%), Minnesota Sen. Amy Klobuchar (5%), businessman Tom Steyer (3%) or entrepreneur Andrew Yang (3%). Interviewing for the poll finished on Friday night, as the Democratic debate got underway, so the survey does not reflect any reaction to that debate.

Buttigieg's gains come almost entirely at Biden's expense. He has gained ground among two critical pillars of Biden's support: Older voters (Buttigieg is up eight points among those age 45 and older, while Biden drops nine points) and moderate and conservative voters (up six points while Biden falls 5).

Though Sanders' overall numbers are largely steady, he has solidified his backing among younger voters (up eight points among those under age 45) and liberals (up 10 points among that group). The shift among liberals seems to sting Warren most directly, as her backing with that group has dropped six points to 15%.

And a majority of likely primary voters in New Hampshire say they expect Sanders to win on Tuesday (56% say so, up from 39% in the January poll).

For Biden, this poll brings mostly bad news. Beyond Buttigieg slicing into his core support, his advantage on having the best chance to win in November -- the driving argument for his campaign -- has disappeared since mid-January. While 41% two weeks ago saw him as most likely to beat President Donald Trump , now, just 25% say the same. More likely New Hampshire primary voters now say they will not vote for him under any circumstances (17%) than said so at any point in UNH's polling on this question in the last year. And just 10% say they think he's most likely to win in New Hampshire on Tuesday, down 12 points since January.

Sanders' lead over Buttigieg rests largely on a 14-point advantage among the roughly half of likely primary voters who say they have made up their minds about whom to support.

Among the movable half who say they are leaning toward a candidate or have yet to choose one, Buttigieg (21%) and Sanders (19%) are about even, with Warren (11%) and Biden (8%) well behind.

Those movable voters are more apt to say they have ruled out Warren (15%), Biden (14%) or Sanders (10%) than to have crossed Buttigieg off their list (2%).

On the Republican side, Trump continues to trounce -- 91% say they will back him, just 5% choose former Massachusetts Gov. Bill Weld

The CNN New Hampshire Poll conducted by the University of New Hampshire Survey Center was conducted February 4 through 7 among a random sample of 365 likely Democratic primary voters and 203 likely Republican primary voters. Results for likely Democratic primary voters have a margin of sampling error of plus or minus 5.1 percent. It is plus or minus 6.9 points among likely Republican primary voters.