The proposal was on the table in earlier deficit negotiations, and President Obama also included it in his 2013 budget proposal.
Liberals have pressed the White House to ditch the so-called "blended rate" since the Supreme Court's landmark healthcare ruling this summer. The Supreme Court said states must have the ability to opt out of the healthcare law's Medicaid expansion.
Proposals to shift more costs to the states wouldn't be very helpful as the White House tries to convince states that federal funding for the new expansion is secure. HHS acknowledged as much when it said it no longer supports the blended Medicaid rate.
"The Supreme Court decision has made the higher matching rates available in the Affordable Care Act for the new groups covered even more important to incentivize states to expand Medicaid coverage," HHS said in a questions-and-answers document to governors. "The Administration is focused on implementing the Affordable Care Act and providing assistance to states in their efforts to expand Medicaid coverage to these new groups."