WASHINGTON – The fight over the contraception mandate in the health care law will not likely determine which party wins the White House and Senate in the fall.

But Republican Sen. Roy Blunt of Missouri has played a leading role in ensuring that it becomes part of the campaign debate. In a year when political margins in many contests are expected to be close, his efforts could have an impact.

The Senate is expected to vote Thursday on Blunt’s measure to repeal an Obama administration rule requiring most health insurers to cover contraceptives for women. He wants to allow employers and insurers to deny coverage for health care services beyond birth control if those companies have either religious or moral objections.

While Republicans have publicly supported Blunt, some are anxious about the growing role of cultural issues in the campaign.

In close contests in battleground states such as Pennsylvania and Ohio, the votes of moderate Republicans and independents — particularly women — in places such as suburban Philadelphia and Cleveland could be pivotal. Unlike with Republican primary voters, cultural issues are often not their paramount concern.

Asked this week whether her party should be focused on the contraception mandate, Republican Sen. Lisa Murkowski of Alaska said: “I don’t think so. I think we’ve got way too much to be doing.”

Republican White House hopeful Mitt Romney said in an Ohio television interview Wednesday that he opposed the Blunt amendment.

“I’m not for the bill, but look, the idea of presidential candidates getting into questions about contraception within a relationship between a man and a women, husband and wife, I’m not going there,” Romney said.