The first part of his bet is that he can persuade the Legislature, which is split by regional rivalries and under pressure from competing gambling interests, to place a referendum on the ballot authorizing such casinos. The governor quite likely has only a few days — the Legislature is scheduled to adjourn for the year on Thursday — and he will then have to persuade the state’s voters, who are currently split over casinos, to approve the referendum, most likely in November. And even then, Mr. Cuomo will have to persuade casino companies to make big investments in upstate New York, a region that has been regarded with skepticism by some developers and industry analysts.

None of these challenges, it seems, have dulled the governor’s enthusiasm for casino gambling, which he promotes as a bold move to bring jobs and tourism to economically depressed regions, thus addressing a problem that has dogged New York leaders for decades.

“If you want tomorrow to be different than yesterday, then do something different,” Mr. Cuomo, a Democrat, said in announcing one version of his plan in May. “This is a big idea that we believe could bring economic energy to upstate New York that needs it desperately.”

New York already has five full-scale casinos, all run by Indian tribes upstate, and the state also allows limited electronic gambling at nine racetracks, including Aqueduct Racetrack and Yonkers Raceway, both of which are highly successful. Mr. Cuomo wants the Legislature to ask voters to allow as many as seven full-scale, nontribal casinos, but said that over the first several years there would be fewer, and all of them would be upstate.

The prospect of expanded gambling in New York has sparked an avalanche of spending by the gambling industry. In 2011 and 2012, gambling interests spent $17.8 million on lobbying and political contributions, up 36 percent from the previous two years, according to an analysis by Common Cause.

But not all of that money is supporting expanded gambling. Operators of the slot parlors at nine racetracks spent nearly $10 million in Albany, and those groups are seeking either to obtain casino licenses themselves, or prevent others from getting them.

The New York State Gaming Association, which represents the racetrack slot parlors, said last week that it would not support the governor’s legislation. But negotiations have continued, and over the weekend the governor introduced a new twist: he proposed to allow more slot parlor operators in New York City if a referendum failed.

The governor’s spokeswoman, Melissa DeRosa, said that, absent approval of upstate casinos, more city slot parlors would “combat the loss of revenue to neighboring states and secure new funding for our schools.” But new slot parlors would also mean more competition for the existing racinos. “No racino was granted a lifetime monopoly,” Ms. DeRosa said. “We were elected to act in the best interest of the people, not politically connected racino owners.”

Mr. Cuomo has already used the prospect of expanded gambling to find more revenue for the state, brokering three recent deals with Indian tribes to settle contract disputes and other issues. The deals, most recently with the Seneca Nation, will bring the state hundreds of millions of dollars from the tribes in exchange for geographic exclusivity.

The debate over casinos is likely to become even more complicated if the Legislature agrees to put the referendum on the ballot. Myriad deep-pocketed state and national players would most likely be involved in any fall referendum battle, and it remains unclear how much of a campaign against the measure opponents of expanded gambling would muster.

Mr. Cuomo, who failed last year in his plan to build a $4 billion convention and expanded gambling complex in Queens, appears eager to make a deal this year. On Friday, he said he would consider issuing four casino licenses upstate, up from his original three, in a possible effort to appease lawmakers from the Catskills, a former resort area with a depressed economy. (Hours after the governor’s shift, Senator John J. Bonacic, a Hudson Valley Republican who is chairman of the Senate Committee on Racing, Wagering and Gaming, suggested there should actually be five upstate casinos.)

Even if expanded casino gambling is approved by the Legislature and by voters, it is not clear how many casinos can obtain financing and survive in lesser populated upstate areas.

Mr. Cuomo has said he imagines “resort gaming destinations” — complete with hotels, shops, entertainment venues and four-star restaurants — upstate. He would allow casinos — in the short term — in three regions, including the Albany region, the south-central area bordering Pennsylvania, and the Catskills. The Catskills, in particular, have long appealed to some casino developers, including the The Mashantucket Pequot Indians, who own the Foxwoods casino resort and who announced last week a desire to build a $500 million casino resort in Liberty, N.Y.

Among the optimists are Emanuel R. Pearlman, chairman of Empire Resorts Inc., which operates a slot parlor at the Monticello Raceway, about 90 miles northwest of Manhattan. Mr. Pearlman said his company — which has ties to the same Malaysian family that controls Genting, the megacasino company — had received preliminary approval to build a resort that would include a water park, a new racetrack and, he hoped, a casino.

“We are hopeful that it will be the catalyst to stimulate the redevelopment of the Catskills,” Mr. Pearlman said.

Executives from Caesars, a big name in the casino world, have toured upstate cities and are interested in a location outside of the Catskills. But several other major casino companies that specialize in large-scale developments — including Wynn Resorts, Las Vegas Sands and MGM Resorts — insist that they are only interested in building casinos in or around New York City. “The money is where the tourists are,” said the Rev. Richard McGowan, an adjunct associate professor of economics at Boston College who writes about the gambling industry.

Mr. Cuomo has argued that upstate casinos could create tens of thousands of jobs and hundreds of millions in investment. But Alan R. Woinski, the president of Gaming USA Corporation, which publishes industry newsletters, said, “You’re not going to get people to invest a billion and a half, two billion dollars upstate. Because you’re not going to get the return on it.”

Mr. Woinski and other analysts noted the problem of potential casino saturation in the Northeast, where there are now dozens of places to gamble. Casinos in Atlantic City and Connecticut have seen revenues fall steadily as legal gambling has proliferated in the region. Revenues at the 12 casinos in Pennsylvania have been hurt by the Yonkers and Aqueduct slot parlors, as well as by new casinos in Ohio and Maryland. And slots, craps and roulette are on the way in Massachusetts, which is in the process of licensing three casinos.

Any referendum campaign would likely involve education funding; the racinos, which pay a tax rate of more than 60 percent, much of which is earmarked for education, contend that they will have a hard time competing with the new casinos, which Mr. Cuomo has suggested would pay a 25 percent tax rate. That, the racinos say, means there will be less money generated for education. The administration disputes that, saying that more revenue will be produced under their plan.

A Quinnipiac poll earlier this month showed 48 percent of voters support amending the Constitution to allow expanded casino gambling. Support was weaker in New York City — a problem for advocates of expanded gambling, because the mayor’s race in New York means turnout in the city is likely to be higher than in other parts of the state this year.