What does 'Become a scarlet letter' mean for a Senator who took advantage of the ‘Tea Party’ wave in the mid-term election?

I came across a phrase, senators who become a scarlet letter, in an article of today’s Washington Post (Jan.29) titled "Tea Party Caucus holds first meeting without some who had embraced banner."
The sentence in question reads as follows:

The Republican senators who rode the tea party wave to victory in the fall are now weighing whether that label will help them on Capitol Hill or become a scarlet letter.

I understand scarlet letter means the letter of A in red signifying adulterer, and it was used as figurative expression by all means. However in this case, I'm puzzled with whom (i.e. political group, faction, clique) do the Senators in question commit adultery, and who is their due (should-be) partner (husband or wife, i.e electral franchise or belonging clique)? Why can they be dabbed a scarlet letter? I read the whole article, but I couldn't figure its meaning out to the end. Can anybody explain?

As you stated, the "scarlet letter" was the letter A that Hester Prynne was made to wear in The Scarlet Letter to signify that she was an adulterer. In the book, she is treated as a social pariah (outcast) because of the letter. Most people would not associate or interact with her unless they had to, and when they did it was with a look of disgust.

In the sentence you quoted, the implied meaning is that Republican senators who proclaimed themselves to be a part of the Tea Party are now trying to figure out if it will help them or if it caused them to become outcasts with regard to their fellow Republicans as well as citizens in general.

The sentence uses scarlet letter as a metaphor; it doesn't use the phrase to mean the senator is an adulterer.

The sentence should be understood as

The Republican senators who rode the tea party wave to victory in the fall are now wondering if having ridden the tea party will help them on Capitol Hill or have a negative effect.

I suspect it's yet another cliche that people don't know what it actually means.

Avoid it like the plague.