Sen. Lamar Alexander continued to rail on the Affordable Care Act Thursday, announcing he has signed on as a co-sponsor of a bill that would delay employer and individual mandates until 2015.

The bill, called the Fairness for American Families Amendment, was introduced by Senate Minority Leader Mitch McConnell, R-Ky.

Referencing July's delay of the employer mandate, a key provision of the law, Alexander said families should receive the same treatment.

"Full repeal of this law is my goal," Alexander said in a news release. "No family in Tennessee should ever be forced to comply with the mess and mistakes of Obamacare—but I hope even Democrats will be willing to see that families certainly shouldn't have to [comply] next year when American businesses are getting a break."

Thursday's news was the latest in a string of releases and campaign advertisements by Alexander touting his opposition to the new law.

The senator, who is also up for re-election in 2014, has faced an onslaught of opposition from both state and national conservative groups for his support of government funding bills, including, among many other items, monies for implementation of the law.

In the past, Alexander has supported continuing resolutions approved in order to avoid a shutdown of the government. The senator has said that despite a campaign to "defund Obamacare" by opposing a continuing resolution this fall, he would not vote against it for the sole reason of delaying implementation of the health law—a position shared by his Tennessee colleague Sen. Bob Corker.