The House supported SB 193, passed by the Senate last year but changed substantially by the House Education Committee, leading to the 1 84-164 vote on January 3rd. The bill now goes to the House Finance Committee, which has scheduled its public hearing for January 16 at 1:30 in room 210-211 of the Legislative Office Building (right behind the State House).
After that, the Division II committee (one of three permanent subcommittees that do the detailed work in preparing bills for consideration of the Finance Committee) will work on the bill and bring it back to the full committee for a vote in, probably, late February or March.
It is entirely possible, even likely, that the Finance Committee will amend the bill. They could do anything from recommending Inexpedient to Legislate based on the large and undefined cost to the State to amending the bill to limit cost. Or the committee could send it to study committee.
Whatever the result is in the Finance Committee (other than sending it to study), the bill will come back to the House floor for another vote. If it passes, it will go back for another vote by the Senate, since it will now be a bill much changed since the Senate passed it last year. The Senate could pass the House bill and send it to the Governor for signature (there is little doubt that he would sign it). More likely, the Senate would want further changes, which could result in conference committee before further House and Senate votes. If the same bill does pass both houses at any point, it will go the the Governor for signature.