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 FischerIvanka Trump turns to House GOP on paid family leave GOP senators pleased with Ivanka Trump meeting on family leave, child tax credits McCain threatens to block Trump's deputy Defense nominee MORE and Ted CruzTed CruzGOP ObamaCare fight faces do-or-die procedural vote Conservative groups hammer Senate healthcare reform bill The Memo: Trump seeks to put his stamp on nation 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.