Releases sent out by Senate Democrats hit Republicans running for the Senate in Louisiana, Georgia, Montana and West Virginia. 

The committee charges that the candidates are supporting attacks on women's rights rather than working to find a way to avoid a government shutdown.

Tom CottonThomas (Tom) Bryant CottonThe Hill's Morning Report - Lawsuits, investigations send Trump on Twitter tirade GOP senator: Democratic opposition to Pompeo 'driven 100 percent by politics' Sunday Shows Preview: Emmanuel Macron talks ahead of state dinner MORE’s [R-Ala.] recklessness and partisanship clearly has no limit. Instead of focusing on the economy and working to avoid a government shutdown, Tom Cotton is waging a war to roll back health care rights for thousands of Arkansas women,” Justin Barasky, a spokesman at the Democratic Senatorial Campaign Committee, said in the release targeting Cotton. 

Religious groups and certain employers have expressed opposition to the inclusion of free birth control coverage in ObamaCare, arguing that groups that oppose not be forced to offer it. 

Democrats believe women's issues will again play well for them in the 2014 elections, after a sizable gender gap helped boost Democratic candidates nationwide, as well as President Obama, in 2012.

In a blog post responding to the attacks, National Republican Senatorial Committee spokeswoman Brook Hougesen noted polling that indicates women overwhelmingly — and to a greater extent than men — oppose ObamaCare, and suggested it is in fact Democrats who are needlessly focusing on women's issues rather than working on avoiding a shutdown.

"Washington has been dysfunctional for 5 years under Democratic control, yet as the government moves closer to shutdown, Democratic men are focused on birth control and sex rather than making sure the government doesn't shut down. Attention Democrats: Women don't want the government to shut down and overwhelmingly don't want ObamaCare," she wrote.

— This post was updated at 1:34 p.m. to reflect comment from the NRSC.