Yet while Americans seem to have clear opinions on the shutdown, Cruz is a much less defined figure. In a poll from Quinnipiac University released last week, almost 60% of Americans said they did not know enough about Cruz to have an opinion about him. Among those who did, opinions were slightly more negative than positive.

Democrats working on the Virginia governor’s race tested Cruz’s name in a focus group with roughly 30 undecided voters race this past weekend, according to a person familiar with the session, which was held in the Washington suburbs where the shutdown’s impact is felt most acutely.

According to the source, Cruz was not a well-known personality among the voters. But when the Democratic operatives described Cruz as a tea party leader with a prominent role in the shutdown, and said he was appearing with Cuccinelli at the gala Saturday night, impressions of both men soured among the focus group participants.

Some Republican pragmatists, already worried that emboldened conservative hard-liners are tarnishing the party’s brand, acknowledge that Democrats appear to have found a potent weapon in Cruz.

David Kochel, a 26-year veteran of Iowa politics who managed Mitt Romney’s presidential campaign in the battleground state, said bluntly that “swing voters are repelled by Cruz.”