House Republicans are attempting to win key Democrats over as supporters of a major overhaul of the mental health system as the legislation approaches a significant hurdle.

An updated version of the GOP’s reform bill is slated for mark up in the House Energy and Commerce health subcommittee Thursday. Author Rep. Tim Murphy (R-PA) submitted the new version this week with strategic revisions designed to address Democratic criticisms. Among the changes: Rewriting certain sections that would alter the rights of the mentally ill under the Health Insurance Portability and Accountability Act (HIPAA), and revising the process for awarding federal funds to states that do not have laws that would allow the courts to force certain individuals into mental health treatment programs.

The news source The Hill said that Murphy has been in discussions with other committee members, and said the revisions reflect the substance of those conversations.

But, The Hill reported, Democrats initially expressed skepticism about whether the alterations to the major legislative initiative truly addressed their core concern: that longstanding rights to privacy and self determination for the mentally ill would be swept away, forcing millions into treatment programs they might not need or benefit from.

The bill first surfaced in 2013 following the mass murders in Newtown, Connecticut. Strong Democratic opposition has kept the bill at bay to date.