King would begin with 34 percent support to 19 percent for Latham. Iowa Lieutenant Gov. Kim Reynolds (R) pulls 10 percent and Christian conservative leader Bob Vander Plaats (R) pulls 9 percent, according to the poll. In a pure head-to-head matchup, King leads Latham by 43 to 35 percent.

Both congressmen have been considering a bid. Latham said on Monday that whether King runs or not wouldn't affect his own decision on the race.

The poll's numbers should be taken with a few caveats.

Citizens United often backs conservative candidates in GOP primaries, and while the poll's release doesn't say who they might support and they've backed both King and Latham in the past, it's unclear why the group would be polling the race and releasing private polling numbers unless they were looking to boost King.

Wenzel Strategies also had an uneven track record in 2012, like many Republican pollsters: Their polls showed GOP candidates leading in races they ended up losing, including Mitt Romney, former Rep. Todd Akin (R-Mo.) and former Wisconsin Gov. Tommy Thompson (R). They did, however, do much better in primaries, predicting before other pollsters that GOP Senate candidates Richard Mourdock, Deb FischerDeb FischerLawmakers share photos of their dogs in honor of National Puppy Day Senators demand Pentagon action after nude photo scandal GOP rep scolds Gillibrand for tearing into Marine general over nude-photo scandal MORE and Ted CruzTed CruzTrump: 'No doubt' we'll make a deal on healthcare The mystery of Ivanka Trump Wounded Ryan faces new battle MORE had momentum.

The poll of 800 GOP likely primary voters was conducted Feb. 1-2 and has a margin of error of plus or minus 3.44 percentage points.

This post was updated at 11:58 a.m.