ALBANY — The Democrats who control the State Assembly, many of them black or Latino residents of New York City, saw a proposal to decriminalize the open possession of small amounts of marijuana as a simple matter of justice: too many black and Latino men were being arrested because, after being stopped by the police, they were forced to empty their pockets.

But the Republicans who run the State Senate, all of them white and most of them from suburban or rural districts, saw decriminalization differently: as an invitation for young people to use drugs and as a declaration that Albany was soft on crime.

“Marijuana still is a gateway drug to so many other much more dangerous things,” said Senator John J. Flanagan, a Long Island Republican.

The differing life experiences, and worldviews, of lawmakers in the two chambers proved too much to overcome in the final days of this legislative session, and on Tuesday, Gov. Andrew M. Cuomo declared his marijuana proposal dead.

Mr. Cuomo, a Democrat, said: “You have old folks like me who say, ‘Whoa, the decriminalization of marijuana: What are you saying? Everyone is going to walk around smoking marijuana, and that’s O.K.?’ So I think the Senate got a lot of blowback, pardon the pun.”

The demise of the proposal came amid a last-minute push to tie up loose ends before the close of the session, which is scheduled to conclude on Thursday. All legislative seats are on the ballot in the elections this year, and Republican senators have pointedly refused to take up several issues that are avidly sought by Democrats in the Assembly but that might upset conservatives, including the marijuana bill and a measure to raise the state’s minimum wage.

Mr. Cuomo unveiled his marijuana proposal two weeks ago, promoting it as a way to end the high number of arrests that result from the stop-and-frisk practice of the New York Police Department. He immediately won the backing of Mayor Michael R. Bloomberg, as well as the department and prosecutors.

With the support of law enforcement, some Democrats and drug-policy advocates said they did not expect the Republican-controlled Senate to stand in the way.

“You have the governor of the state, the speaker of the Assembly, the mayor of the city, the police commissioner, all five D.A.’s from the city,” said Harry G. Levine, a sociologist at Queens College who has studied the city’s marijuana arrest practices. “It seemed like if this many powerful people said they wanted X, which wasn’t that big a deal, it should be possible to do it.”

But the collapse of the marijuana proposal illustrated an at-times awkward reality about the balance of power in Albany: Legislation eagerly sought by New York City can easily be torpedoed by lawmakers from upstate, even when the legislation largely affects only residents of the city.

The marijuana measure would have had an impact mostly on city residents because, of the more than 50,000 low-level marijuana arrests in New York State last year, 9 in 10 occurred in the city, according to state data.

In private discussions about the marijuana bill, Senate Republicans raised concerns about the amount of marijuana that Mr. Cuomo’s bill would have allowed people to possess in public without being charged with a misdemeanor — 25 grams. By one calculation, that would produce 63 marijuana cigarettes — one for each member of the Senate next year, as a Republican senator joked at a discussion of the proposal.

The Senate majority leader, Dean G. Skelos, a Long Island Republican, said Tuesday that it was possible the Senate would revisit the marijuana issue next year, and he denied that he felt political pressure to block the bill.

“All I know is my son was thrilled to see me on ‘The Daily Show,’ ” Mr. Skelos said, referring to a television segment that lampooned his resistance to the measure.

But supporters of the marijuana proposal were not pleased. Assemblywoman Rhoda S. Jacobs, a Democrat who represents Flatbush, Brooklyn, said Republicans were blinded by ideology and ignoring the likelihood that their own constituents used marijuana. “Their posture and the way they are perceived is to be very law and order,” she said. “Everybody who’s got a college kid probably is turning a blind eye to the fact that kids are experimenting.”

Mr. Cuomo, who has at times been accused of not paying enough attention to the concerns of black and Latino lawmakers, won widespread applause for tackling the marijuana issue and, in doing so, giving more public attention to the growing criticism of the Police Department’s stop-and-frisk tactics.

But Assemblywoman Inez D. Barron, a Democrat representing East New York and parts of Canarsie and Brownsville in Brooklyn, said the governor had not pushed the issue vigorously enough in the past two weeks.

“It’s not a critical issue to him, but it is for our communities, and we understand it,” Ms. Barron said. “I believe that he’s playing a game of trying to enhance his political stature by not pushing the Republicans. He doesn’t want to expend a political favor by asking them to really come forth and support this bill.”

Speaking to reporters on Tuesday, Mr. Cuomo argued that his marijuana bill was the kind of proposal, like same-sex marriage, that would take time to persuade lawmakers to support.

“Many of the large issues, social issues, they don’t happen over a period of weeks,” he said. “It takes a period of months, sometimes a period of years.”