State election laws dictate that Southampton Town Supervisor Linda Kabot will be the Republican candidate for Southampton Town supervisor on the November ballot. And Ms. Kabot has said she has no intention of resigning her post, or suspending her reelection campaign, in the wake of her arrest in Westhampton Beach last week for DWI after refusing to submit to a Breathalyzer test.

But how will the charges against her impact both her reelection bid over the next seven weeks, and her ability to conduct the business of the town for the remaining months of her current term, or beyond? It is a question that many of her supporters dismiss, but some of her colleagues and local political experts say it will be a nagging one.

Ms. Kabot’s continued refusal to discuss her arrest publicly, now more than a week after the fact, has drawn criticism from many veteran political players, some of whom said this week that such a refusal may actually be more detrimental than the arrest itself.

Ms. Kabot pleaded not guilty and has said she will fight the charge, hinting that she was wrongly arrested and refused a breath test because she thought the officers were being overzealous in their belief that she was drunk. She has said her attorney has advised her not to make any public statements about the arrest.

But veteran political players say that regardless of the legal ramifications, not discussing the proverbial elephant in the room is not a wise move politically.

“When you are in the public eye, you do have a responsibility to explain things, even personal things, to the public—they have a right to know,” former Southampton Town Councilman Steve Kenny said this week. “I know she has legal counsel, but that doesn’t play in the public eye, particularly when you’re a month or two away from people passing judgment on you. You either have to explain yourself or apologize—whichever is appropriate.”

State Assemblyman Fred W. Thiele Jr., himself a former two-term Southampton Town supervisor, said he has seen public figures survive charges similar to those faced by Ms. Kabot, though typically under somewhat less pressing time constraints and almost always after publicly airing the issue. In 1997, Assemblywoman Susan John was charge with DWI while serving as chairwoman of the Assembly’s committee on alcohol and substance abuse—she won reelection and still serves in the Assembly.

“People are forgiving,” Mr. Thiele said. “But she’s going to have a difficult time, because it’s two months until the election. Most of the people I know of in this situation were a year or 18 months away from the election, and they had the opportunity to redeem themselves. The other thing they did, almost universally, was to be extremely contrite and take responsibility for what they did—and that may be the missing element for Linda Kabot.”

No matter what the public’s reaction, Ms. Kabot will be on the November 4 ballot. In the days after her arrest, speculation swirled about whether she would withdraw from the race; whether the Republican Party, which had only reluctantly adopted her as the party candidate after political wrangling on her part forced a last-minute change on the ticket, would seize on the arrest as reason to oust her; or whether she might even resign before the election.

State law answered the first two questions, and Ms. Kabot dismissed the last in short order. After the July deadline for candidate petitions had passed, it was too late for the Republican Party to change its candidate roster, whether it wanted to or not. And in the wake of the arrest, the party faithful have at least made an attempt to show public support for their candidate.

Ann LaWall, a member of the Republican Party’s executive committee, acknowledged that there are local Republicans who have not supported Ms. Kabot’s headlining the party ticket and saw her arrest as reason enough for the party to give up.

“Linda has made some enemies,” Ms. LaWall said. “How can you be in politics and not? It’s to be expected. But she’s a tough kid ... and she is our candidate, no matter what.”

The party’s top brass were all at a fund-raiser for Ms. Kabot’s campaign at Oakland’s Restaurant and Marina in Hampton Bays last Thursday night. Party Chairman Marcus Stinchi, who is giving up his position at the end of this month, was among the more than 100 people at the fund-raiser, as was his heir apparent, Ernie Wruck, Town Board candidate Jim Malone—who was the Republican committee’s initial choice for its supervisor candidate—and several other party veterans.

Some of her most loyal supporters even hinted that Ms. Kabot’s arrest might have been politically motivated.

“The way it was done, it was perfect timing—it was politically timed,” Tony Cenzoprano, a Hampton Bays resident who attended Ms. Kabot’s fund-raiser, said of her arrest. Mr. Cenzoprano said he didn’t think the charge will hurt Ms. Kabot’s reelection bid: “Everyone sees through it. She stepped on toes, but for the right reasons.”