In Jean Hay Bright’s estimation, she’s two for two.

Hay Bright, a Dixmont Democrat challenging Republican U.S. Sen. Olympia Snowe, took heart in Tuesday’s Rhode Island Republican primary win by Iraq war opponent Sen. Lincoln Chafee.

Chafee’s win, she said, along with last month’s Democratic primary loss by U.S. Sen. Joe Lieberman in Connecticut to his anti-war challenger, bodes well for her own bid to unseat Snowe.

“New England voters on both sides of the aisle – both Democrats and Republicans – are sending the clear message to their parties that it is time for this war to stop,” Bright, an author and organic farmer, said in a statement Wednesday . “It is a message that needs to be repeated at the polls on November 7.”

Chafee voted against the Iraq war in 2002. Snowe – and Lieberman – voted in favor.

But while Hay Bright paints Snowe as a “war hawk” for that 2002 vote, and subsequent votes to fund the conflict, Maine voters have been loyal to the senior senator – one of the most popular in the country, according to tracking polls.

And while the war is likely to play a role in some midterm elections, said Richard Powell, a political scientist at the University of Maine, it would be a mistake to overestimate its ability to decide any particular race.

“The war is clearly unpopular, but in congressional races, it is going to be one of many factors,” Powell said. “That’s not to say the war won’t come into play in some close races, but for the most part these races are fought on local concerns.”

Snowe spokesman Lucas Caron on Wednesday also downplayed the war’s impact on the Rhode Island race, which gained national attention for its potential to change the makeup of the Senate.

“The long and the short of it is that the Rhode Island race was not a referendum on the war in Iraq,” Caron said. “It was a choice between a moderate Republican and a much more conservative Republican, and at the end of the day, the voters there chose to put forth a gentleman who reflects mainstream values.”

In that race, Chafee defeated the conservative mayor of Cranston, R.I., Stephen Laffey, 55 percent to 45 percent.

Chafee, like Snowe, is considered one of a handful of moderate New England Republicans in the Senate. Both have bucked the president – and their party – at times, most notably on the Bush administration’s tax cut proposals.

In 2004, Chafee voted with his fellow Republicans 65 percent of the time. That year, Snowe voted with the GOP 71 percent, according to Congressional Quarterly.

But in her Wednesday release, Hay Bright noted that Snowe supported Bush administration policies 82 percent of the time during the president’s entire first term. Snowe’s first advertisement, Hay Bright noted, doesn’t reference the war – or Snowe’s political affiliation – once.

“Snowe is running away from her party, but only in her ad,” Hay Bright said.

Powell said it is common for candidates to omit their party affiliation from ads leading into a general election, so as not to alienate independent voters or even voters from the other party.

Caron said neither omission – a mention of the war or her party – was intentional. The first ad, Caron explained, was a way to reintroduce Snowe to voters. Issue ads, such as one dealing with the war, he explained, were likely forthcoming.

As for Snowe’s GOP ties, “she is proud to be a Republican,” Caron said.

The race also features an independent – and another anti-war candidate – in Bill Slavick of Portland. He could not be reached for comment for this story.