ALBANY Nine months ago, when he was the lieutenant governor, David A. Paterson dreamed that Senator Hillary Rodham Clinton would head to the White House and he would be tapped to fill her Senate seat.
Now Mr. Paterson, who became governor in March after Eliot Spitzer resigned, will be the one picking a replacement for Mrs. Clinton, who is said to be poised to become the next secretary of state.
On Friday night, just before delivering a speech to the N.A.A.C.P. in San Francisco, Mr. Paterson told reporters that 10 to 20 people had already contacted him about their interest in taking Mrs. Clinton’s place. “I would say it’s not a shy and retiring group of people who would like to serve in the Senate,” he said, declining to name them. “It’s almost distracting me from trying to close the very severe deficit of nearly $15 billion in New York.”
Mr. Paterson has not begun a formal search, and there is not even a short list, advisers said. The only thing he has ruled out is appointing himself, which some have said would amount to abandoning the state amid a fiscal crisis.
“New York State residents have been through enough drama this year,” he said on Friday night.
Earlier this week, Mr. Paterson said, “I am the governor of the State of New York, and I want to run for re-election as governor in 2010.”
Picking a replacement for Mrs. Clinton is full of consequences for New York. She has been a high-profile advocate for the state’s interests and would be leaving at a time when the state has been lobbying for more federal aid as its financial engine, Wall Street, hemorrhages. She has been a formidable campaigner for Democrats, not just by winning her two Senate elections handily but in stumping for local lawmakers across the state.
Mr. Paterson’s appointee would have to run in the 2010 election and again in 2012. If he picked someone without an established political network, that person might be seen as an attractive target for Republicans, who have few openings in New York.
The governor and his staff have been informally discussing whom he might pick and what criteria they would like a potential senator to meet. They were aware that Mrs. Clinton was a likely pick for President-elect Barack Obama’s cabinet days before the news became public last week. But Mr. Paterson has not given any inkling of whom he might select.
One person close to the governor said, “He is not in the process of working through names or anything like that.” And Risa B. Heller, his communications director, said, “It’s premature to comment without an official announcement.”
Among the governor’s inner circle, there is a desire to pick someone from upstate New York, since the region has no representation in statewide office. A woman or a Latino would also be desirable; discontent among Hispanic lawmakers has led to a leadership struggle in the State Senate.
Still, on Friday night, Mr. Paterson said that he would “not be able to serve all these interests with one appointment.”
That said, the most high-profile potential candidate is Attorney General Andrew M. Cuomo, who has won praise during his two years in office. A Marist College poll had Mr. Cuomo comfortably leading a field of five potential replacements. Representatives Nydia M. Velázquez, Steve Israel, Nita M. Lowey and Gregory W. Meeks were all in single digits, while 43 percent of respondents favored Mr. Cuomo; 42 percent were unsure.
“Andrew would be an obvious choice, but I would be surprised if he wanted the job since he loves getting things done as attorney general,” said one person close to Mr. Cuomo.
The Marist poll excluded those who are likely to get serious consideration, aides said. One is Representative Kirsten E. Gillibrand, a lawmaker from Hudson, whose district stretches across 10 upstate counties. A former corporate lawyer, Ms. Gillibrand is seen as smart and appealing, if inexperienced she has served only two years in the House.
Other contenders include Adolfo Carrión Jr., the Bronx borough president, and two men from the Buffalo area Representative Brian Higgins, whose district stretches to the Pennsylvania border, and Mayor Byron W. Brown of Buffalo. Less expected choices include Caroline Kennedy, who most recently worked on Mr. Obama’s campaign.
One twist to consider: If Mr. Paterson were to pick Mr. Cuomo, it would be the duty of the entire Legislature to choose Mr. Cuomo’s replacement. It would be the second time in two years that the Legislature has had to fill a statewide office.
Nineteen candidates sought the Legislature’s backing to replace Alan G. Hevesi as comptroller when he resigned shortly after being re-elected in 2006. More than one state legislator has run for attorney general in the past, and there would no doubt be a wide open and spirited fight to replace Mr. Cuomo.