Sen. Ted Cruz Rafael (Ted) Edward CruzTrump argues full Supreme Court needed to settle potential election disputes Press: Notorious RBG vs Notorious GOP The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy MORE (R-Texas) has edged his way into third in the early voting state of Iowa, according to two new polls released Monday.

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A separate poll of Iowa released Monday by the left-leaning Public Policy Polling also found Cruz in third place behind Trump and Carson, with 14 percent support.

Cruz and Rubio have battled for third place in a series of polls in the state recently. Both received positive ratings after the GOP debate last week in Colorado aired by CNBC.

But Cruz had perhaps the most memorable moment of the debate when he attacked the CNBC moderators for trying to turn the contest into a "cage match."

The questions, he said, “illustrate why the American people don’t trust the media.”

Cruz was among several Republicans in Iowa over the weekend attending an annual pheasant-hunting fundraiser hosted by Rep. Steve King (R-Iowa). Rubio also held campaign events in the state over the weekend.

The latest poll finds Carly Fiorina at 4 percent in Iowa and New Jersey Gov. Chris Christie, Ohio Gov. John Kasich, former Arkansas Gov. Mike Huckabee and Sen. Rand Paul (Ky.) each at 2 percent.

The survey of 874 likely Republican caucus-goers was conducted immediately after last week's debate Oct. 29-31 via landlines and cellphones with a margin of error of 3.4 percent.

— This story was updated at 4:41 p.m.