Rep. Dean Heller (R-Nev.) is locked in a statistical dead heat with Rep. Shelley Berkley (D-Nev.) in the race for retiring Sen. John Ensign's (R-Nev.) seat, according to a new poll out Tuesday.

The latest numbers on the Nevada race from Democratic-leaning Public Policy Polling found Heller up 47 percent to 43 percent over Berkley, which is within the poll's margin of error. The last time PPP surveyed the race in early January, Heller was up nine points.

Heller's numbers are largely as result of strong support among independent voters — the Republican holds a commanding 56 percent to 29 percent advantage among independents.

The poll also found Republicans largely unified around Heller, who gets 86 support among his own party. That's 10 points higher than Berkley's party support. Berkley earned 76 percent among Democratic voters, and she faces a largely unknown but well-funded primary challenger in businessman Byron Georgiou.

Democrats, however, see an opening in the uncertainty created by Ensign's departure. Gov. Brian Sandoval (R) will name Ensign's replacement by May 3, and most expect him to appoint Heller. That could touch off a special election for Heller's House seat, which Democrats are already lobbying against.

Some Democrats in the state are highlighting the potential cost of a special election in urging Sandoval not to tap Heller for the post. State elections officials are also still sorting out a state statute that doesn't make the process for filling Heller's potentially vacant House seat clear.