Plenty of “L” words will be used to describe Democratic Rep. Tammy Baldwin in Wisconsin’s closely watched Senate race – “liberal,” “left,” “labor” – but “lesbian” is not likely to be one of them.

If Baldwin wins, the seven-term Congresswoman would be the nation’s first openly gay Senator. But to date, the race that could decide the balance of the Senate has steered clear of social issues – including Baldwin’s sexual orientation. That is why an email last week from her opponent’s political director questioning her “heartland values” and featuring a video of Baldwin at a 2010 gay pride parade caught so much attention.

Former Gov. Tommy Thompson (R) has publicly distanced himself from the email, which was fired off from an official campaign account in response to Baldwin’s speech last Thursday at the Democratic National Convention. Thompson told reporters Tuesday he “thought it was a mistake” and that his aide “shouldn’t have done it.”

The incident, however, underscores the difficulties Republicans could face if they, or anyone else with enough money to run ads, try to make sexual orientation an issue in the race. Baldwin always has run as an openly gay candidate, beginning with her successful state Assembly bid in 1992. And the American public is evolving in its views of the gay community. The Democratic-leaning Public Policy Polling found last month that 64 percent of the state’s voters are open to supporting a gay candidate for office.

“Let’s be clear here, Tammy Baldwin is a lawmaker who happens to be lesbian. She is not a lesbian lawmaker,” said Fred Sainz, the vice president of communications for the Human Rights Campaign, a lesbian, gay, bisexual and transgender advocacy group.

Sainz, who said the HRC is paying particular attention to Baldwin’s race, noted that candidates or campaign surrogates who try to use their opponents’ sexual orientation against them do so “at their own peril because we are in a period of great transition in this country in terms of how people think about gay and lesbian equality” and that Thompson’s distancing himself from his aide was “certainly a measure of progress.”

But just because Republicans aren’t highlighting Baldwin’s sexual orientation doesn’t mean they’re not trying to paint her as an out-of-touch outsider from the most liberal city in the state.

Nearly every statement released by Republicans refers to Baldwin as “Extreme Madison Liberal Tammy Baldwin,” mostly in reference to her voting record being among the most liberal in the House.

“The Thompson campaign has consistently stressed Baldwin’s liberal voting record in Washington, and so we’re going to see a campaign that paints her as a very liberal, out of touch with the state outside of Madison – and there’s a lot of things wrapped up in that, potentially including her sexual orientation,” said Charles Franklin, the director of the Marquette Law School Poll and visiting professor of law and public policy at the university. “But it’s very hard to suss out how much that plays a role, above and beyond ideology.”

Sainz, for his part, disputed that the GOP’s “Madison liberal” tag for Baldwin has anything to do with her sexual orientation.

“It’s something that is used an awful lot of times,” Sainz said. “I used to live in Colorado, if Mark Udall was called a Boulder liberal one more time, I was going to throw up.”

From a strategic perspective, attacking Baldwin personally could be risky. Overly personal attacks – like that from the campaign of former North Carolina Sen. Elizabeth Dole (R) charging that Democrat Kay Hagan was a “godless heathen” – have not only backfired, but also arguably decided elections for their targets.

“My impression, just watching a lot of the ads around the country is that the really nasty campaign ads that are over the top really backfire,” National Republican Senatorial Committee Chairman John Cornyn (Texas) said, adding that the campaign in Wisconsin, like those across the country, will be focused on the economy.

Cornyn, who said he was “not aware” of the Thompson aide incident, said establishment Republicans likely would not pursue a line of attack based on Baldwin’s sexual orientation but that it is still possible one of the many, well-funded outside groups could wage a campaign on the issue in the Badger State.

“Well that’s one aspect of our broken campaign finance system is yes, anybody who is able to raise money can come in and essentially hijack the campaign, that’s where we are,” Cornyn said. “So the candidate can’t control that.”

Thompson has been strapped for cash after a bruising primary – he held a fundraiser in Washington, D.C., on Wednesday night pulling $1,000 to $5,000 per person, according to an invitation obtained by Roll Call – and has yet to go on the air with ads against Baldwin.

It remains to be seen whether his campaign will run character ads, though if the campaign chose to do so it would not be without provocation. Baldwin’s campaign has been running attacks against Thompson, questioning his post-gubernatorial life, his ties to lobbyists and his refusal to release tax returns.

Sources say that Thompson’s public repudiation of his aide’s behavior, while positive and necessary, still leaves questions over whether his position is the one maintained by his entire staff and his supporters statewide. In an interview with the Milwaukee Journal Sentinel, the Thompson aide responsible for the email did not specifically express regret that he sent it. Attempts to reach Thompson’s campaign for comment were unsuccessful.

It’s still difficult to say how much sexual orientation ultimately will factor into voters’ decisions, mostly because there’s not an abundance of data available and because Thompson is averaging a 9-point advantage over Baldwin.

The Marquette poll has not tracked Badger State views on gay marriage this year, but it’s a question that likely will be included in a poll to be released next week.

“The open question is whether a gay candidate who has always been openly gay can compete statewide, and a separate issue is whether a liberal candidate from Madison can develop issues that appeal to voters throughout the state on policy ground separate and independent from sexual orientation,” Franklin said.