It’s interesting that the White House rolled this one out just after Mitt Romney’s drubbing in three contests yesterday — one that was largely driven by Romney’s inability to connect with social conservatives.

At the press briefing just now, White House press secretary Jay Carney twice highlighted the fact that as Governor of Massachusetts, Romney supported a contraception policy that was very similar to the one Obama has now adpoted, to much criticism.

Romney has been attacking Obama over the issue, and Carney was asked to respond.

“The former governor of Massachusetts is an odd messenger on this, given that the services that this rule would provide for women around the country are the same as those that are provided in Massachusetts, and were provided when he was governor, including contraception,” Carney said.

“It’s ironic that Mitt Romney is criticizing the president for pursuing a policy that’s virtually identical to the one that was in place when he was governor of Massachusetts,” Carney added.

A reporter asked Carney whether this meant the White House agrees with Rick Santorum on the issue. This was intended as a joke, but it’s actually pretty meaningful, and goes to the heart of what the White House is accomplishing here.

By pointing out the similarities between Obama and Romney on contraception, the White House is in effect giving Romney a social issues death hug. Carney, inentionally or not, is encouraging a dynamic that could further damage Romney in the GOP nomination process: The better Santorum does, the more social issues will come to dominate. And the more Romney has to move to the right on them, in a campaign he had bet would be all about the economy, and at a time when Romney had hoped to be moderating his image in preparation for the general election.

This social issues death hug is similar to the health care death hug that the White House gave Romney some time ago by pointing out the similarities between Romneycare and Obamacare. But in some ways social issues could be more problematic.

As Ronald Brownstein noted today, the three contests Romney lost to Santorum last night contain ominous signs for him, because social conservatives dominate in all of them. And in all three of them, the number who came out to vote for Romney dropped sharply from four years ago. So Romney’s struggles to make headway with social conservatives will continue.

Even if Romney is still the favorite for the nomination, the more the debate shifts towards social issues, the worse it could get for his overall chances. With the economy improving, and with the controversies over contraception and Proposition 8 flaring up, that may be what’s happening, to Romney’s detriment.

It’s a dynamic the White House seems happy to encourage in whatever way it can.