AUGUSTA — Independent candidate for governor Eliot Cutler has challenged Democratic nominee Mike Michaud to release his voters to Cutler prior to Election Day if Michaud does not think he can beat Republican Gov. Paul LePage.

The Michaud campaign reacted incredulously to the challenge and said it’s Cutler — who has consistently polled 20 points behind his rivals — who is keeping LePage’s chances alive. Cutler did preface his challenge to Michaud by saying he would encourage his supporters to vote for another candidate if they did not think he could win on Election Day.

Cutler’s challenge to Michaud, which he first made in a forum Thursday night and then again in a news release Friday morning, is part of an ongoing effort by the Cutler campaign to plant doubt among Michaud supporters about the congressman’s chances of defeating LePage.

There is little evidence to support the notion that Cutler’s campaign is seeing a surge. A poll conducted online by the BDN and Ipsos between Oct. 6 and 12, showed Michaud with a lead and Cutler with 16 percent support, about where the independent has been for months. Poll aggregators continue to put Michaud and LePage on average within one point of each other.

And new poll results released Friday morning by Public Policy Polling show Michaud and LePage locked at 40 percent support and Cutler at 17 percent, which is consistent with just about every poll so far in this race. The poll surveyed 660 likely voters on Wednesday and Thursday of this week and has a margin of error of 3.9 percent.

The poll is the first to reflect voter attitudes following the debates and following some newspaper endorsements for Cutler, including from the BDN. Among other things, the Democrat-leaning pollster predicted that Michaud would beat LePage in a hypothetical one-on-one matchup.

Cutler has been hoping all along that voters would swing to him in the final weeks of the campaign, after they saw him take on the Democrat and Republican in a series of debates that concluded Tuesday.

“Maine voters have increasingly come to realize that Mike Michaud can’t close the deal with voters,” Cutler said in Friday’s release. “He can’t win, whether I’m in the race or not.”

Cutler and LePage have attacked Michaud relentlessly, and groups normally affiliated with Republican causes have directed financial support at Cutler in apparent attempts to turn voters away from Michaud.

LePage, whose support has never wavered from within a few percentage points of the 39 percent of the vote he received in 2010, criticized Cutler far less often than he did Michaud in debates and continues to assert that he would beat Michaud in a one-on-one race.

On Friday, the Maine Democratic Party pointed out that ultra-conservative donors James and Marilyn Hebenstreit of Kansas have donated to Cutler’s campaign directly and recently gave $50,000 to the Campaign for Maine PAC, which backs Cutler. The Hebenstreits have a long history of financial support for Republicans, according to the Democratic party. The Campaign for Maine on Thursday reported an expenditure of $15,000 for television ad production.

David Farmer, a senior adviser to the Michaud campaign, said Cutler is trying to create a narrative that isn’t there.

“That’s like the Boston Red Sox calling on the Kansas City Royals to drop out of the World Series even though the Sox didn’t even make the playoffs,” Farmer said in a written statement. “U.S. Rep. Mike Michaud is the only person who can beat Gov. LePage, a fact that’s confirmed by all the public polling to date and reinforced by the fact that Republicans are propping up the Cutler campaign.”