For much of the past year, Clinton has held a comanding lead in the polls in her adopted home state, and it would be a stunning collapse if Sen. Barack Obama of Illinois were to make the New York race competitive.
"I've got a lot of people working very hard for me," Clinton said. "And if voters ask themselves who they think would be the best president, and if Democrats ask who they think would be the best candidate to win, I feel really good about the answers to those questions."
In New York, the Democratic winner doesn't take all, and the primary is expected to be a rich source of delegates even for second place. New York has the second-most delegates at stake on Tuesday, behind California.
There are 232 Democratic delegates: 151 will be split based on the vote in each of the state's 29 congressional districts and the remaining 81 will be divided based on the statewide popular vote. A Democratic candidate must get 15 percent of the vote in a congressional district to earn delegates.
On the Republican side, Sen. John McCain of Arizona and former Massachusetts Gov. Mitt Romney are considered the leading candidates for the winner-take-all haul of 101 delegates.
State election officials declined to give any early numbers on turnout. In upstate Erie County, Democratic Commissioner Dennis Ward said turnout seemed light to moderate.
Some voting machines jammed in parts of Brooklyn, but the problem was quickly remedied, said Valerie Vasquez, spokeswoman for the New York City Board of Elections. Any voters affected were given paper emergency ballots that were included in Tuesday's vote count.
This year's choice was difficult for some New York City Democrats. At polling locations in Brooklyn's Cobble Hill section - a bastion for the left - voters pondered who was more electable in middle America: A black man or a white woman?
Some liberals drawn to Obama's campaign had second thoughts and voted for Clinton, because they thought her centrist message would play better in the general election. Some feminists who have waited their whole lives to vote for a woman agonized as they cast their vote for Obama instead.
"I was torn for a long time. In the end, I kind of went with my gut," said Danielle Tarantolo, 28, after casting her vote for Obama. Tarantolo, a lawyer, said she bypassed Clinton because she thought Obama would do better in the general election. "I know too many people, Republicans and independents, who still hate her. And if they haven't changed their minds by now, they probably never will."
In the Democratic stronghold of south Buffalo, N.Y., Paul Dissek, 63, waited alone in the fog outside a library for the polling place to open at 6 a.m.
With health insurance his biggest issue, Dissek was voting for Clinton. The retired Bethlehem Steel worker spent 34½ years at the plant only to lose his coverage a year after he retired in 2001. He's covered now, but has to pay.
"I lost my health insurance with the steel plant. I figure she'd be the one to get it," he said.
Republicans in New York are painting McCain as a "straight talker" who would curb federal spending, protect the borders from illegal immigrants and who was the sole voice supporting the military "surge" of troops in Iraq that has turned the war around.
"There is no one who is more dedicated. There is no one who is more conscientious," said state Senate Republican leader Joseph Bruno at a McCain rally Monday. "There is no one who is more committed to the benefit of the people of New York and the whole United States than Sen. John McCain."
Stephen Piccininni of Chappaqua said he voted for McCain, adding that Rudy Giuliani's decision to drop out and endorse McCain was "not very important" to his decision.
"I wasn't a Giuliani supporter, although I respect him. McCain had the most experience," Piccininni said. "He and I generally agree on the issues. McCain is able to say what has to be said. He's someone who knows the process and I think has the right solutions for Iraq and the economy. He's the right guy for that."
Romney brings the most private sector experience to the race and says McCain doesn't understand the economy. Romney has made that his top issue, along with pressing his conservative social views - which can be critical in a GOP primary.
Mike Huckabee, a Southerner and one-time Baptist preacher, is trying to emerge as the more conservative alternative to McCain.
A statewide poll released Monday showed Clinton's long unassailable popularity among New York Democrats is eroding. The Quinnipiac University poll showed her 2-to-1 lead over Obama two weeks ago has shrunk to a 53 percent to 39 percent edge.
For Republicans, Monday's poll showed McCain extended his lead over Romney, the former Massachusetts governor, 54 percent to 22 percent.
New York moved its primary up to join this year's Super Tuesday group of states conducting nominating contests. In the past, it was held later in the cycle when nominations were already locked up.
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Associated Press writers David B. Caruso in New York City,
Carolyn Thompson in Buffalo, N.Y., and Jim Fitzgerald in Chappaqua,
N.Y., contributed to this report.
