Legalization of medical marijuana is head­ed for a vote by the full state Senate on Tuesday.

The proposal, which would allow marijuana to be used for a broad range of ailments and set up a statewide system of dispensaries, cleared its last Senate hurdle on Monday. The Senate Finance committee approved the bill 14-7.

“We have the votes to pass it,” predicted Sen. Scott Dibble, DFL-Minneapolis, the bill’s chief sponsor.

The effort for legalization had been in limbo for much of the session, stymied by a powerful set of opponents: Gov. Mark Dayton and the law enforcement community. But shortly after Dayton told legislators to “quit hiding behind their desks” on the issue, the proposal was revived and began racing through committees, picking up momentum to make Minnesota the 22nd state in the nation to legalize some version of medical marijuana.

Should the bill pass the Senate, it would still face a serious obstacle in the House, where a much narrower proposal is being considered. The House version would tightly regulate medical marijuana, restricting its use to patients eligible for a clinical trial. Vaporized marijuana could be used only in the presence of a health provider. There would be only one provider and no system of dispensaries. Law enforcement and Dayton have appeared willing to consider the House bill, but remain opposed to the Senate version.

The Senate bill would allow patients with qualifying conditions to get a doctor’s prescription for up to 2.5 ounces of marijuana. Eligible conditions would include can­cer, HIV/AIDS, glau­co­ma, ep­i­lep­sy, post-trau­ma­tic stress dis­or­der and sev­er­al con­di­tions that cause chron­ic pain. Pa­tients would not be able to smoke mar­i­jua­na, but could use a vaporizer to inhale fumes. The could also ingest the drug in pill or oil form.

State budget officials estimate the state would have to spend about $3 million in 2015 to implement the Senate’s version of legalization. Those costs would be covered by fees related to purchase of the drug. The state budg­et of­fice an­aly­sis pre­dict­ed about 35,000 Min­ne­so­tans would par­tici­pate in the new program, a figure that Dibble contended was too high.

The House Ways and Means Committee was set to review the House bill on Monday evening. A floor vote in that chamber could also come this week.

In the Senate Finance Committee, voting in support of the measure were: Dibble, DFL Sens. Dick Cohen of St. Paul, Ter­ri Bonoff of Minnetonka, Bobby Joe Champion of Minneapolis, Ron Latz of St. Louis Park, Tony Lourey of Kerrick, Sandy Pappas of St. Paul, Tom Saxhaug of Grand Rapids, Kat­ie Sieben of Newport, Le­Roy Stumpf of Plummer, David Tomassoni of Chisholm and Chuck Wiger of Maplewood, along with Re­pub­lic­ans Scott Newman of Hutchinson and Sean Nienow of Cambridge.

Voting against the bill were Re­pub­lic­ans Bruce Anderson of Buffalo, Mi­chelle Fischbach of Paynesville, Bill Ingebrigtsen of Alexandria, Warren Limmer of Ma­ple Grove, Jer­e­my Miller of Winona, John Ped­er­son of St. Cloud and Tor­rey Westrom of Elbow Lake.