ALBANY - Defying Gov. David A. Paterson's request, State Senate Majority Leader Malcolm Smith will not put a bill legalizing same-sex marriage to a vote without first knowing whether there is sufficient support for passage. Paterson, in unveiling the legislation last week, said it should be put to an up-or-down vote so senators' positions would be known. But Smith (D-St. Albans), who supports gay marriage, told reporters he wanted to line up the required 32 votes, or possibly 34, before allowing the bill onto the Senate floor. Meanwhile, a poll released Monday showed that more than half of state residents want the Senate to authorize gay marriage. Support was strongest among young people, women, Democrats and independents. Fifty-three percent of voters surveyed by the Siena Research Institute said the Senate should pass Paterson's bill. The Senate has been the stumbling block; the Assembly passed a similar measure in 2007. Thirty-nine percent were opposed to same-sex marriage, including a majority of Republicans, men, older voters, blacks and Protestants. Eight percent didn't express an opinion. On Long Island and in the other New York City suburbs, support for gay marriages between two men or two women was 51 percent for and 42 against. "By a fairly significant margin, voters would like to see New York join with Vermont, Massachusetts, Iowa and other states in allowing same sex couples to marry," said pollster Steven Greenberg. Asked about the results, Paterson said, "We didn't put out the bill because of what the polls would say. We put the bill out because there are 1,324 protections that people who are married receive." Smith spokesman Austin Shafran said, "these new poll numbers further validate our support for marriage equality legislation. Senator Smith is fully committed to continuing the process of securing the 32 votes necessary for passage and ensuring that all New Yorkers can enjoy the fundamental right of marriage equality." Later Monday, former New York City Mayor Rudy Giuliani said he backs civil unions, but not gay marriage. He said the GOP must focus on the economy, not social issues, to regain power in state government. "The Republican Party is best to organize itself around economic issues and issues of national security; we end up getting back to being a majority party that way," he said. Paterson unveiled the legalization bill Thursday. Four Democratic senators have stated their opposition and the 30-member Republican conference remains opposed. For the bill to pass the 62-member Senate, it must garner 32 affirmative votes. Last week, Smith told reporters at a meeting of the state Democratic Rural Conference, "I'm very concerned about putting a bill on the floor that's going to be symbolism and not pass. . . . I'm going to count until I know that I have 32, if not 34, votes." Smith acknowledged needing Republican support, but said he was "not going to get into horse trading" to win passage of the bill. His comments were first reported Monday on the Daily News Web site.