Republicans were more likely than Democrats to say their support for a candidate was contingent on the candidate’s position on the Affordable Care Act.

Image Senator Kay Hagan spoke with the press after a recent event in Durham, North Carolina. Credit... Jeremy M. Lange for The New York Times

Attention to the campaigns is low, the polls found. Less than one quarter of each state’s voters say they are paying a lot of attention. Still, about three-quarters of the voters say they will definitely vote in November, and support for Republican candidates for both the House and the Senate is generally higher among those paying more attention to the campaign and more likely to vote.

“If we keep on the path we’re on, the United States is headed down the path of socialism,” said Lou Jaquith, 73, a Republican retiree from Lexington, Ky., in a follow-up interview.

Voter opinions on the health law appear to be less polarized in Kentucky, where the Democratic governor has overseen a widely praised implementation. In that state, voters were relatively more open to backing a candidate whose view on the Affordable Care Act differs from theirs.

Image Thom Tillis is one of eight Republican candidates looking to unseat Kay Hagan in the North Carolina Senate race. Credit... Jeremy M. Lange for The New York Times

Democrats, while conscious of the structural challenges in these red states, are hopeful that the nature of the Republican races in each state will help their candidates. If Mr. Tillis does not get 40 percent of the vote in next month’s primary, for example, he will face a runoff in July against a candidate running to his right. The presence of other Republicans in the Louisiana Senate race means Mr. Cassidy will have to balance appealing to conservatives with making the case against Ms. Landrieu among more moderate voters. And while Mr. McConnell is expected to win his primary next month, Matt Bevin’s Republican challenge has partly diverted Mr. McConnell’s attention from Ms. Grimes.