ALBANY — After adopting a $175.5 billion budget, Gov. Andrew M. Cuomo and legislators are deciding what’s next from a list that includes the long shot of single-payer health care; the more likely protection of renters that could be extended statewide, the uncertain prospects of legalization of marijuana, and the wild card of whether to provide driver’s licenses to immigrants in the United States illegally.

“Now that the budget season is over — that was the first half,” said Assembly Speaker Carl Heastie. “Now is the second half.”

Those hoping marijuana would be legalized in the post-budget session are facing an uphill battle at best. Cuomo, leading legislators and pro-marijuana lobbyists sought to include the measure in the state budget, which was adopted Monday. That would have allowed the controversial measure to be tied to many other popular issues, including more school aid, and increasing its likelihood of passing.

Cuomo on March 19 pulled the issue — and the $300 million in tax revenue it promised — off the budget table. At the time, Cuomo was desperate to add revenue to the budget and address a $3 billion deficit and declining revenues, but he said legislative leaders made it clear that the complex issue of legalizing marijuana wasn’t going to be resolved in time for the budget deadline.

The question then turned to whether the measure could be passed as a stand-alone bill after the budget. “This legislative session? I don’t know,” Cuomo said.

At the time, several legislators said there didn’t appear to be enough votes in the Senate for the measure to carry on its own. Since December, influential groups, including the state Medical Society, the county health commissioners and law enforcement, stepped up to strongly oppose legalization.

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A leading advocate in the Legislature for legalization isn’t betting on approval coming by the scheduled end of the session on June 19.

“I don’t know how it gets done now, now that it’s in the open,” Sen. Diane Savino (D-Staten Island) said in an interview. She noted other states have found legislating the legalization of marijuana difficult.

Although eight states and the District of Columbia have legalized marijuana in recent years, each was done through voter referendums. Vermont is the only state to legalize marijuana through its legislature, but that 2018 law remains a work in progress. Vermont allows possession of only small amounts of marijuana and this year is still trying to determine how it can be sold and taxed. Law enforcement continues to wrestle with enforcing a law on driving while impaired at a time when there is no widely accepted way to measure driving while high.

Politically, however, there will be still be pressure to legalize marijuana from a legion of advocates and a wave of Democrats who campaigned last fall on the promise.

“We believe that New Yorkers deserve more than unmet promises and empty rhetoric around marijuana reform,” said Kassandra Frederique, state director of the Drug Policy Alliance. “It is also time for Governor Cuomo to keep his commitment to marijuana reform, and the justice that he has promised. The clock for passing marijuana justice starts now.”

If Albany’s past behavior is any indication, however, legalizing marijuana may have a better shot as part of a traditional “big ugly” at the end of session. As in the budget, many popular items are often tied to unpopular ones in a last-day omnibus bill, often voted on at night with little public notice.

Among the issues that could be part of a big ugly or be a major stand-alone vote this session is rent control. This temporary law traditionally protects rent-controlled apartments and their tenants, most of whom live in New York City along with many on Long Island and some upstate. It expires this year.

“We’re going to be laser-focused on rent regulations and not just in the city across the entire state,” said Heastie (D-Bronx). “There is 20-some years of history in rent regulation that I think has to be fixed,” Heastie said. Rent-controlled apartments were created decades ago to provide for affordable homes for middle class residents.

The issue itself, part of temporary law requiring extension every three or four years, has dominated previous legislative sessions.

This year, however, will be different. Heastie’s plan to extend the tenants’ rights to the suburbs and upstate could make the issue a statewide concern.

“One of the most important priorities is certainly housing,” said Sen. Gustavo Rivera (D-Bronx). “It is incredibly essential that we get that right.”

Cuomo said, “This is going to be a great reform for tenants, and I believe we will get more people than we’ve gotten before.”

Progressives in the Democratic-controlled Senate and Assembly are also pushing for a showdown with Cuomo and their own leaders over the goal of a single-payer health care system. In the budget, the state codified Obamacare, which should at least for a time protect New Yorkers from threatened cuts coming from the White House.

But the goal for many progressives is an overhaul of health care to a single-payer system they say would cover all New Yorkers affordably.

Assembly Health Committee chairman Richard Gottfried (D-Manhattan) said he recently had conversations with the Cuomo administration on this concept, which he’s pushed for years. He is now joined by a cadre of new, progressive colleagues in both chambers.

“Single-payer is the only one that makes sense,” Gottfried said.

Standing in the way, however, is the cost. Some have estimated it in the billions, although Gottfried and other supporters say the program will be more effective and save billions. One of the goals of the hearings and debate this year would be to find a common ground on the cost, legislators said.

Another major issue of lobbyists and unions that are major funders of political campaigns will decide whether to require a higher “prevailing wage” be required on all jobs that include any state funding. Most traditional public works must pay this prevailing wage, which tracks with union wages, but the state under Cuomo has increasingly used public-private partnerships in which private contractors do the hiring.

“There is a dispute now as to what threshold the prevailing wage would kick in,” Cuomo said. “I want to propose a compromise that if we can’t get it done, we let the (state) Department of Labor set those standards.”

Cuomo also said he would exempt builders of low-income housing from paying a higher wage “because you can make a case that it increases the costs of construction.”

Another issue for which the volume is already turned up is the possibility of providing driver’s licenses to immigrants who came to the United States illegally.

A dozen states as well as the District of Columbia issue licenses to those in the country illegally. Even the federal REAL ID program, which is aimed at providing better ID cards to combat terrorism, have allowed states to offer driver’s licenses to those immigrants, as long as they are clearly marked as not being suitable for federal identification purposes.

New York progressives don’t want to see the state falling behind, but the complexity of the issue and fear by many legislators that it would provide terrorists entry to sensitive sites has long made agreement elusive.

Legislators are also looking closely at state revenues after the April 15 income tax deadline. After months of declining revenues, they are hoping for a rebound. If that happens, it would likely set off another fiscal fight with Cuomo, whose budget is already being criticized by the fiscally conservative Empire Center think tank as spending too much with too little in reserve.

“There might be an opportunity to restore some issues that fell off the table,” said Assemb. Deborah Glick (D-Manhattan). She had sought to raise funding for the Tuition Assistance Program, which hasn’t adjusted its income eligibility in a decade.

Other progressives agree there is more to do, and spend.

“We are going to try to do as much as we can for the rest of the legislative year to continue to show we are a responsible legislature that wants to move progressive issues forward,” Rivera said.