Former President Bill Clinton's Obamacare message for Democrats is simple: don't run away from it.

In an interview with Real Clear Politics earlier this week, Clinton drew upon his own experiences, saying that shying away from the Affordable Care Act is not the answer.

"I thought that Democrats had a tendency to shy away from things they had done that were unpopular, (and) talk about positions they had that were popular," Clinton said. "And that my own experience had convinced me -- going back to '94 and even more when I was governor -- that that was always a terrible mistake. That you had to turn in toward all controversies and embrace them -- even if you said you were wrong or a mistake was made. You couldn't not deal with it."

Clinton's remarks arrive amid Thursday's news that Obamacare enrollments had surpassed six million. Those numbers fell ahead of Obama administration projections, with a few days to go before the March 31 enrollment deadline.

The former president's remarks also offer a stark contrast from the advice of top Democratic pollster Celinda Lake. Earlier this week, Lake told onlookers at a Christian Science Monitor breakfast that vulnerable 2014 Democrats should tread carefully on the health care law.