Unlike the others who face election in 2014, Heitkamp was just elected to a six-year term. Begich was considered more secure politically than Pryor and Baucus, and thus a less attractive target. Baucus announced Tuesday that he will not seek re-election.

That leaves Pryor as possibly the lone target of a campaign to convince Democrats that there is a price to pay for opposing modest gun regulations, even in a conservative-leaning state like Arkansas.

The broader goal of the Bloomberg group is to provide a political counterweight to the National Rifle Association which has had virtually unmitigated influence over Congress since 1994, when Democrats lost control of the House and blamed then-President Clinton’s assault-weapons ban.

The Bloomberg group is mulling a variety of messages and methods for Arkansas. One approach would be to target reliable Democratic voters, including African Americans, with advertising that calls out Pryor for “opposing the president’s agenda,” the official said. Another would be to expand the campaign to suburban women and other moderates. The campaign might not be limited to the issue of guns.

“Money would not be an object,” the official said, adding that a decision on whether to target Pryor would come soon and that action against other Democrats is still possible.