Updated 4:45 p.m. | A new poll conducted for former Rep. Heather Wilson (R) shows the New Mexico Senate race could be more competitive than currently believed — if a third-party candidate does well on the November ballot.

In the survey, Wilson was in a virtual tie with Rep. Martin Heinrich (D), who took 43 percent to Wilson’s 42 percent. But Independent American Party candidate Jon Barrie took 9 percent, and 6 percent of respondents were undecided. The poll, conducted by GOP pollster Glen Bolger, was in the field Tuesday through Thursday and sampled 500 likely voters. The margin of error was 4.38 points.

But even as the Wilson campaign released this poll showing its candidate back in contention, the Heinrich campaign put out its own survey that showed the Congressman’s commanding lead holding steady at 52 percent to 44 percent. This survey, by Democratic firm GBA Strategies, was conducted Monday through Wednesday and had an error margin of 4 points.

However, Heinrich’s poll was a head-to-head with Wilson and did not include Barrie.

Bolger, in a polling memo for the Wilson campaign, argued that “Barrie is getting double digits among Independents and Democrats” and “clearly taking votes away from Heinrich.” Bolger also notes in the memo that GOP presidential nominee Mitt Romney trailed President Barack Obama 47 percent to 40 percent, with Libertarian Gary Johnson, the former Republican New Mexico governor, drawing 9 percent.

Republicans were excited early on by Wilson’s prospects. But most recent polls have shown her trailing Heinrich significantly. Roll Call rates this race Leans Democratic.

UPDATE 4:55 p.m.

The Heinrich campaign responded to Wilson’s latest poll showing Barrie boosting the Republican’s competitiveness with numbers of its own. According to polling conducted for the Democratic candidate, Barrie still garnered 9 percent in a three-way contest. But in Heinrich’s survey, he led Wilson 48 percent to 40 percent.

“The 3-way match-up likely overstates Barrie’s support, but it makes no difference,” the polling memo from the Heinrich campaign read.