The announcement that Jill Stein will run for governor on the Green Party ticket is generally seen as another headache for Deval Patrick, who can’t afford to lose any votes to his left in this fall’s election. Stein, who got 3 percent of the vote and respectful press coverage when she ran for governor in 2002, is probably the strongest possible candidate for her shrub-like political party, and she’s likely to get votes from people who aren’t happy with Patrick’s performance but who would never vote Republican.

Still, likely Republican nominee Charlie Baker would be wise to keep an eye on Stein. Her geographic base is in the more affluent parts of MetroWest Boston, which is precisely where Baker needs to peel some votes away from Patrick (much in the way that Mitt Romney made gains in this region). As long as she stays under 5 percent, her vote probably comes out of Patrick’s hide; anything more, and things could get dicey for the GOP.

There’s also the fact that Stein may end up as a strange bedfellow with Baker, his fellow Republican candidate Christy Mihos, and independent Tim Cahill on the issue of the state’s sales tax. All three of those candidates want to repeal last year’s sales tax hike from 5.0 to 6.25 percent (Mihos wants to push it down to 3 percent), and Stein said last summer that she was also against the sales tax hike — on the grounds that it was regressive and that a graduated income tax was the better way to go.

It’s not clear whether Stein will make a sales tax rollback a priority of her campaign (as the GOP nominee and Cahill surely will), but it would be interesting to see Patrick stand alone in defending last year’s tax hike (and, indirectly, the Legislature that passed it). Would he look like the voice of fiscal sanity, or would he stand out for being more politically tone-deaf than the lefty Greens?