House Democrats blew a chance at a top pickup opportunity in California in 2012 — and might be at risk of doing so again, according to a new poll.

Three Democrats are splitting the vote for retiring Rep. Gary Miller's (R-Calif.) seat, raising the prospect that two Republicans might be able to advance in the all-party primary, according to a poll conducted for the Democratic Congressional Campaign Committee and obtained by The Hill. The district is Democrats' top pick-up opportunity this election cycle.

Redlands Mayor (and DCCC-backed candidate) Pete AguilarPeter (Pete) Ray AguilarMcCarthy dismisses push for vote on immigration bills Immigration fight gets lonely for some in GOP GOP lawmaker says he has enough support to force immigration votes MORE (D) is at 15 percent in the live-caller poll, from Democratic firm Tulchin Research. Former Rep. Joe Baca (D-Calif.) and attorney Eloise Gomez Reyes (D), who's backed by EMILY's List, are tied at 13 percent.

Former White House official Paul Chabot (R) is at 23 percent in the poll. Former Miller staffer Lesli Gooch (R) is at 6 percent, but has a big campaign war chest and is just starting to spend to boost her name identification in the district.

Two years ago, a crowded Democratic field, including Aguilar, split the vote, and Miller and another Republican made the top-two runoff, leaving Democrats without a candidate in a district that President Obama won by 17 percentage points in 2012.

The polling memo from Tulchin Research warns of Democrats getting shut out in the June primary once again.

"Absent one of the leading Democrats experiencing a drop in support resulting from a negative attack, the November shutout scenario will continue to remain a real possibility, particularly as long-time Congressional aide and lobbyist Lesli Gooch begins spending down her campaign war chest and communicating with voters," the memo reads. "Research has consistently found that Joe Baca is by far the candidate most vulnerable to negative attack among this primary field."

The poll, first obtained by CQ Roll Call, is a sign that allies of either Aguilar or Gomez Reyes might want to start pounding on Baca, who is a persona non grata at the DCCC and has struggled with fundraising. He has a history of controversial comments about women, and his numbers could drop under attacks.

This post was updated at 8:40 p.m.