The effort includes a petition (which has just over 1,000 signatures at time of publication) and a fundraising drive aimed at preventing Democrats from capitalizing on recent successes, namely the 8 million that have signed up for insurance on the law's private exchanges, as the White House revealed last week.
"The president hopes to turn public opinion around on this issue so 2014 does not become a referendum against Obamacare. We cannot allow this to happen," SCF executive director Matt Hoskins wrote in a fundraising email.
The Democratic senators remain supportive of Obamacare, while calling for fixes to its problems, but haven't made the law a focus of their campaigns. It remains unpopular nationally and the senators have tread carefully with the recent positive news. Democratic candidates in other red state Senate races -- including Michelle Nunn in Georgia and Alison Lundergan Grimes in Kentucky -- have also refrained from touting Obamacare as a major campaign issue.