CHAPPAQUA, New York (CNN) -- First lady Hillary Rodham Clinton overcame a challenge from a Manhattan surgeon to formally claim New York Democrats' U.S. Senate nomination in one of several states to hold primaries Tuesday.
Minnesota Democrats were vying for a chance to challenge a vulnerable Republican incumbent, while in Vermont, a backlash against a state law allowing "civil unions" for gays was expected to drive voter turnout higher. In Selma, Alabama, a 36-year incumbent and former segregationist lost the mayoral primary to his African-American challenger.
In the New York suburbs Tuesday morning, President Clinton said it was a "thrill" to cast a vote for his wife as Mrs. Clinton faced voters for the first time. The first lady is running for the Senate seat being vacated by the retiring Democrat Daniel Patrick Moynihan.
President Clinton signs in at a polling station with U.S. Senate candidate first lady Hillary Rodham Clinton Tuesday as they prepare to vote in the New York Democratic primary near their home in Chappaqua, New York
Mrs. Clinton said she was "surprised, in a way," to see her name in the voting booth.
"I stood there for a minute, staring at my name," she said.
The first lady's challenger, Manhattan surgeon Mark McMahon, said Tuesday that "the Clintons have tried to hijack the Democratic Party."
"This campaign gave the Democratic process back to the voters," McMahon said.
Long Island Congressman Rick Lazio, the Republican candidate for the Senate seat, had no challenger in the GOP primary. Polls indicate the race between Lazio and Clinton in November will be a close one. Barring an upset by McMahon, she and Lazio are set to debate in Buffalo on Wednesday night.
Half a continent away, in Minnesota, State Auditor Mark Dayton led four Democrats in a race to challenge Republican incumbent Sen. Rod Grams. Dayton, a department store heir who has spent at least $5.2 million of his own money on the campaign.
Minneapolis lawyer Mike Ciresi has nearly matched Dayton in spending, with $4.6 million for an equally aggressive ad campaign. State Sen. Jerry Janezich and Rebecca Yanisch, a former Minneapolis economic development official, lag far behind in the polls.
First elected in 1994, Grams is considered one of the most vulnerable Republicans as Democrats push to reclaim control of both houses of Congress for the first time since the 1994 elections.
"The Democrats have been salivating for months at this seat," said Stuart Rothenberg, editor of the nonpartisan Rothenberg Political Report.
In many states, turnout was expected to be low. But in Vermont, a backlash against a state law authorizing "civil unions" for homosexuals is expected to drive more voters to the polls in gubernatorial and legislative primaries. Opponents of the law, which confers some of the same benefits on gay couples that married heterosexuals enjoy, have turned against incumbents who supported the measure.
"It hurts very much," said state Rep. Marion Milne, before Tuesday's vote was counted. Milne, who supported the law, lost the Republican primary to Sylvia Kennedy, a political novice and evangelical Christian who opposes civil unions.
Rep. Milne, who sits among photos of her seven grandchildren at her office in Barre, Vermont, voted in favor of civil unions for same-sex couples this spring
"We've opened a can of worms by creating legislation for a small minority of people," Kennedy said.
A loosely organized movement called "Take Back Vermont" has galvanized opposition to the civil union law. Opposition could even threaten the re-election chances of Democratic Gov. Howard Dean, once considered a shoo-in for a new term.
Dean faces only token opposition on Tuesday, as does incumbent Republican Sen. James Jeffords. Former GOP gubernatorial contender Ruth Dwyer and lawyer William Meub are seeking the Republican nomination for governor.
Four other states -- Arizona, Connecticut, Rhode Island and Wisconsin -- hold congressional primaries Tuesday. In addition, New Hampshire holds a gubernatorial primary; the District of Columbia holds a City Council primary.
Meanwhile, a runoff in Selma, Alabama, unseated longtime Mayor Joe Smitherman, who was seeking a 10th term.
Less than half an hour after polls closed, the former segregationist conceded victory to James Perkins Jr., 47, an African-American computer consultant who had lost two prior attempts to win the mayor's office