Americans were casting their votes for president Tuesday, some lining up hours before polls opened to vote in a hotly contested race that many say is the most important in a generation.

Besides the presidency, voters were filling 34 Senate seats, 11 governorships and all 435 House seats.

President Bush (search), voting in Texas, said, "I've given it my all." Democratic challenger Sen. John Kerry (search), casting his ballot in Boston, promised "a fresh start."

Heavy crowds were reported at polling places throughout the country.

Both parties had pushed to increase turnout among their supporters, and even with early voting in many states, tens of millions were expected to head to the polls on Election Day.

President Bush and First Lady Laura Bush voted at a local firehouse in Crawford, Texas — near their Prairie Chapel Ranch — just after 8:30 a.m. EST.

"The people know I have a vision for this country," Bush said after voting. "These are very troubling times. I believe a president should lead by being very strong and resolute and clear. That's why I'm comfortable about this election. I've given it my all."

Kerry voted in Boston in the early afternoon with his wife, Teresa Heinz Kerry (search), and daughters Alexandra and Vanessa at his side.

"I am very confident that we have made the case for change for new leadership for a fresh start," he told supporters after he'd cast his ballot. "Whatever the outcome tonight, I know one thing that is already an outcome: Our country will be stronger."

After voting, Bush and the first lady traveled to the battleground state of Ohio, where the president thanked supporters in Columbus. The first family returned to Washington, D.C., for the rest of the day and night.

Kerry was traveling back to Wisconsin for a final appearance. He was to return to Boston later to await election tallies.

"I don't think anybody can anticipate what it's like to see your name on the ballot for president," said Kerry. "It's very special. It's exciting."

Heinz Kerry and two of her sons, Chris and Andre Heinz, voted Tuesday near her home in Pittsburgh, Pa.

Vice President Dick Cheney (search) and his wife Lynne cast their votes Tuesday morning in Wilson, Wyo. Democratic vice presidential candidate John Edwards (search) already had voted in his home state of North Carolina.

Former President Bill Clinton, along with Sen. Hillary Rodham Clinton and their daughter, Chelsea, all voted about noon on Tuesday near their home in Chappaqua, N.Y.

The Democratic challenger for the White House spoke to supporters Tuesday morning outside a union hall in La Crosse, Wis., and handed out voting information. The state has same-day registration, meaning residents can both register and vote on Election Day.

"I want to encourage all of you in Wisconsin," Kerry said. "You have same-day registration to vote in this state. Everyone can go out and vote today. You have a choice.

"I'm counting on you," the Massachusetts senator said. "I'm counting on everyone ... tonight we're going to link hands and hearts. Let's get the job done ... I need to get back to Boston to vote."

Bush made reference to the last presidential election, in which the winner wasn't determined for more than a month because of all the recounts and legal challenges that resulted in the extremely close race.

"My hope of course is that this election ends tonight," Bush told reporters, referring to the expected legal challenges in some districts. He won the presidency in 2000 against then-Vice President Al Gore (search) only after a Supreme Court decision gave him Florida and the Electoral College majority.

Of Kerry, Bush said, "I wish him all the best. He and I are in the exact same position ... I'm sure he's happy, like I am, that the campaign is over."

The nation's first Election Day votes were cast and counted just after midnight in a pair of mountain hamlets, with 35 votes for President Bush besting Kerry's 21. Ralph Nader received one vote.

The first Tuesday votes came from the northern New Hampshire community of Hart's Location, (search) where 16 voters chose Bush, 14 went with Kerry and one chose Nader. Minutes later, the 26 registered voters in Dixville Notch (search), about 50 miles to the north, split 19 for Bush and 7 for Kerry.

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Kerry made Election Day appearances in Wisconsin, where residents can register and vote on the same day. Of the reports of long voter lines, he said, "It's just a magical kind of day."

Meanwhile, a federal appeals court cleared the way for political parties to challenge voters' eligibility at polling places throughout Ohio, ruling early Tuesday that their presence on Election Day was allowed under state law. Bush won Ohio in 2000, but is in danger of losing it this election.

Republicans say they wanted challengers in many polling places because of concerns about fraud. Democrats have accused the GOP of trying to suppress Democratic turnout.

Though problems with four voting machines in the Philadelphia area were initially reported by the state Republican Party, city officials dismissed the allegations as totally false.

Republicans said there were votes cast on the machines before the polls officially opened, and called for them to be impounded. But city leaders said some poll workers misinterpreted the number counters on the machines as logging in votes cast Tuesday, when in fact they represented total votes cast since the machines were manufactured.

Philadelphia Mayor John Street told FOX News that the allegations were false, and City Commissioner Marge Tartaglione, the official responsible for overseeing elections there, issued a statement echoing the mayor's remarks.

"Recent press reports have stated that machines in at least one precinct were not properly calibrated to ensure an accurate accounting of the number of votes cast. These allegations are completely unsubstantiated and have no factual basis whatsoever," the statement read.

There were problems in Milwaukee, Wis., with tire slashings of cars that were to be used by Republican get-out-the-vote volunteers, and in Ohio with a woman suing state officials on grounds that some people didn't get their absentee ballots on time.

By all signs, voters were engaged. Those trying to beat the rush turned out early to cast ballots in many precincts as Election Day opened, forming long lines that snaked out the doors, waiting in rain and even taking along chairs for expected long waits.

Umbrellas and raincoats were needed Tuesday from Texas to the lower Great Lakes, and snow-covered roads were a problem in the Texas Panhandle. In some places, voters were standing in line before the polling place doors opened.

At one polling place in a Virginia suburb of Washington — where there was no hotly contested local race to spur interest — nearly 100 people were in line when the polls opened at 6 a.m., in a turnout that one voter said was the largest she had seen in 20 years of voting at the location.

"Every election's important ... but my very survival is an issue, and that never was," said Margie Miller, 55, of Baldwin, N.Y., whose husband Joel died at his 97th-floor desk at the World Trade Center in the Sept. 11 attacks. "All I care about is safety, safety, safety."

Robert Thomas, 21, was among about 150 people in line when the polls opened in Miami at the Mount Zion AME Church, but he said he wished there were more young people there.

"We need to get more young people to vote, like myself," said Thomas, voting in his first presidential election. "I looked around and you see some, but it should be a stronger crowd."

In North Carolina, lines of voters snaked down sidewalks and across a street at a Durham precinct, where one man brought a chair to ease the wait. At a Forsyth County precinct, the first voter in line said he got there before dawn and soon was joined by several hundred more people.

"We wanted to come out early to vote but we never expected such a heavy turnout," Linda Russell said as she stood in line before polls opened in Raleigh, N.C.

Up to 7 inches of snow fell in the Texas Panhandle, and Randall County Clerk Sue Bartolino warned voters to be careful on the roads. A winter weather advisory was posted for the Panhandle and Texas' South Plains, with up to 4 more inches of snow and strong northerly wind expected.

In nearby Texas County, Okla., the earlier arrival of the wintry conditions had led many older voters to turn in absentee ballots on Monday, said Kim Saunders, assistant secretary with the Texas County Election Board.

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Monday Madness

The candidates wrapped up a manic Monday late in the evening after 11th-hour pitches had them scrambling across the country.

Bush visited Ohio, Pennsylvania, Wisconsin, Iowa, New Mexico and Texas, while Kerry hit Florida, Ohio, Michigan and Wisconsin.

The last-minute stumping came as a new FOX News/Opinion Dynamics survey gave Kerry a slight edge.

The poll of 1,200 likely voters, conducted Oct. 30-31, gave the Massachusetts senator 48 percent compared to Bush's 46 percent. Nader got 1 percent support. The numbers were within the 3 percent margin of error.

The previous FOX News poll, released Sunday, put the two candidates at a tie, both with 46 percent. Nader had 1 percent support then as well.

The presidential race also remains tight in four swing states — Iowa, Florida, Ohio and Wisconsin, according to another FOX News/Opinion Dynamics poll released Monday. Bush leads in Iowa, Ohio and Wisconsin, according to this survey, while Kerry has a lead in Florida.

Click here for Tuesday's edition of FOXNews.com's daily campaign digest, Trail Tales.

Both candidates finished up Monday with similar pleas to voters.

"There is a lot at stake in this election. The future safety and prosperity of this country are on the ballot," the president said at a Wilmington, Ohio, airport rally. "Ultimately, though, this election comes down to who do you trust? Who do you trust to make the tough decisions? Who do you trust to lead this country to a better tomorrow?"

His rival said the choice for president should be obvious.

"This is the choice. This is the moment of accountability for America, it's the moment where the world is watching what you're going to do," Kerry said at an airport rally in Orlando. "All of the hopes and dreams, all of the hopes and dreams of our country are on the line today. The choice is clear."

FOX News' Liza Porteus, Catherine Donaldson-Evans, Steve Brown, James Rosen and The Associated Press contributed to this report.