Now come the hard parts.
Republican leaders such as State Senate Majority Leader Dean Skelos of Rockville Centre and County Executive Edward Mangano, who support the plan, are just the headliners in a long list of backers the tribe must enlist to navigate the long and complex processes to secure the site.
At the announcement last week of Nassau County's plan for a new arena with Islanders owner Charles Wang, Shinnecock officials rolled with the latest twist, which followed a year of talks with the county over a now-rejected site at the Nassau Coliseum.
"We have a very quick-moving team that is able to adapt as issues present themselves," said Randy King, chairman of the Shinnecock tribe, which waited 31 years to get federal recognition. Asked if he felt Belmont was a better choice than the Coliseum, he said: "I'm not going to go that far, but you know the county executive is making a very compelling argument. We're excited by it."
The tribe still must win over the administration of Gov. Andrew M. Cuomo -- who last week declined to pledge support for the Belmont plan until he reviews it -- in order to start the process of negotiating a compact with the state. The tribe must settle on a site or sites, and hammer out a revenue-sharing agreement with the state.
A longtime observer of the state political process saw significance in a statement last week by Assembly Speaker Sheldon Silver (D-Manhattan), who said: "We'll look at the merits of the plan . . . and determine if there is any benefit to the state of New York."
"The fact that he didn't rule it out is a significant statement," said the observer, who declined to be named because of a state affiliation.
Much has been said of the difficulties presented to the tribe because of a 2009 U.S. Supreme Court decision restricting federal land-in-trust agreements, which set aside non-reservation land for tribal uses, for tribes that were recognized after 1934. While the Shinnecock tribe was federally recognized last October, it is expected to make the argument that it has long been under federal jurisdiction.
A separate 2009 Interior Department rule says an off-reservation casino must be within commuting distance to the reservation, and approvals by a separate body, the National Indian Gaming Commission, must be won. All told, the approvals suggest the tribe faces an uphill battle in Washington.
But Matthew Fletcher, associate professor at the Michigan State University College of Law and director of the Indigenous Law and Policy Center, said he believes the obstacles presented by the high-court decision can be overcome. "They can argue that they should have been under federal jurisdiction, and actually they were," he said.
A Shinnecock spokeswoman declined to comment.
The tribe also could bypass the federal administrative process in the Interior Department by seeking special legislation with New York congressional delegation sponsors. The move would create a federal land-in-trust pact for the site or sites sought. The tribe would still face lengthy federal environmental reviews.
"You can get land into trust if your congressional delegation is behind you," Fletcher said.
While Rep. Tim Bishop (D-Southampton) has said he would support such legislation, Sens. Charles Schumer and Kirsten Gillibrand have yet to endorse the tribe's goals. Schumer "will carefully evaluate any proposal based on agreements with local and state governments and above all, whether it has broad and deep community support," his spokesman Mike Morey said.
Still, the tribe faces the prospect of congressional opposition from lawmakers in neighboring states, including Connecticut, New Jersey and Pennsylvania, which derive state revenue from casinos there.
And the soon-to-open Aqueduct video-slot parlor, financed by global gaming conglomerate Genting, is expected to have something to say about putting a tribal casino seven miles away. Genting put down $380 million for the right to operate the racino.
What the Belmont site seems to have that many other Long Island locations do not is community support, in addition to political backing. Numerous community groups expressed enthusiasm about the idea.
But not everybody is on board. "I think it's going to create more problems," said Elmont resident Virginia Amato, who lives a few blocks from the racetrack. "It brings more traffic and riffraff into our neighborhood. Who's going to police that?"
Bolstered by state Sen. Jack Martins (R-Mineola), local groups say they welcome a casino as part of a broader Elmont redevelopment they've been pursuing for years. "I'm ecstatic," said Sandra Smith, chairwoman for the Elmont Coalition for Sustainable Development.