Romney led Gingrich by just a 38 percent to 34 percent before the debate, but among those surveyed Tuesday, Romney led by a 10-point margin.

Gingrich said Tuesday that he wouldn't "allow" moderators to silent the audience like NBC's Brian Williams did Monday.

The ARG poll also found Romney with a strong lead among the 233,000 Florida voters who have already cast their ballots. Among those voters, Romney led 51 percent to 39 percent. Those still deciding who to vote for split more evenly, with Romney leading 39 percent to 33 percent.

As has been true in past polls, Gingrich holds a substantial lead with self-identified Tea Party members, while Romney trumps the former Speaker among those who expressly do not identify with the group.