Millions of Americans are voting Tuesday to pick a new U.S. president, deciding whether to elevate Vice President Kamala Harris to become the country's first female leader or return former President Donald Trump to the White House that he lost in the 2020 election.

Polls show that Harris, the Democratic candidate, and Trump, her Republican challenger, are locked in one of the closest contests in decades, with the winner to begin a four-year presidential term in January.

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Political analysts say the national outcome is likely to be determined by the vote in seven political battleground states spanning the country, where surveys show the two candidates are within 2 percentage points of each other, what pollsters describe as a tossup.

Depending on how close the vote is, and how fast the vote counting is in key states, a likely winner could emerge by late Tuesday or early Wednesday, but maybe not for several days, as occurred four years ago.

Both Harris and Trump have assembled a vast roster of experienced election lawyers to contest any irregularities they believe might affect the outcome to their candidate's disadvantage.

Polls opened early Tuesday across the country's eastern states, with people streaming in to vote at government centers, fire stations, schools, churches and elsewhere. Other polling stations opened later across the country's six time zones and by early afternoon polls were open in all 50 states.

Trump, 78, spent the early hours of Election Day in the political battleground state of Michigan. He wrapped up his campaign with a late-night rally in Grand Rapids, a Republican stronghold where he also ended his 2016 and 2020 runs for the presidency.

"We're in very good shape. I have to tell you, we're way up in terms of the vote," Trump declared in a post-midnight speech. He claimed that Harris and the Democrats could only win if they cheat.

"They have to cheat, and they do, and they do it very well," Trump contended. He blamed Harris, as he has throughout the campaign, for high consumer prices and the influx of undocumented migrants across the Mexican border into the United States.

Trump, who cast his ballot in person Tuesday, is spending the day at his Mar-a-Lago estate in Florida. He is scheduled to hold an election result watch party in West Palm Beach on Tuesday night.

Harris, 60, ended her campaign at a star-studded rally in the eastern city of Philadelphia on Monday night, with pop star Lady Gaga, musical groups and former talk show host Oprah Winfrey lending their support.

Harris did not mention Trump in her remarks, telling the crowd, estimated at 30,000, that "tonight, we finish as we started, with optimism, with energy, with joy, knowing that we the people have the power to shape our future."

Harris plans to attend an election night party at Howard University in Washington, a historically Black university where she graduated with a degree in economics and political science in 1986. Harris said Sunday that she had "just filled out" her mail-in ballot and it was "on its way to California," her home state.

Both candidates made stops Monday in Pennsylvania, with 19 electoral votes, the biggest prize among the seven battleground states. They held a series of rallies, with both showing up in Pittsburgh, in the heart of the U.S. steel-making region. Both Harris and Trump expressed optimism.

"The momentum is on our side," Harris told her supporters gathered at a historic steel facility. "Our campaign has tapped into the ambitions, the aspirations and the dreams of the American people. And we know it is time for a new generation of leadership in America."

"We must finish strong," Harris added. "Make no mistake, we will win."

Trump, addressing his supporters at a sports arena, said another presidential term with him at the helm would "launch the most extraordinary economic boom the world has ever seen."

"If you vote for Kamala, you will have four more years of misery, failure and disaster," Trump claimed. "Our country may never recover. Vote for me and I will deliver rising wages, soaring income, and a colossal surge of jobs, wealth and opportunity for Americans of every race, religion, color and creed. Every one of them."

Ahead of Tuesday's Election Day, more than 83 million Americans cast early votes, either in person at polling stations or by mail.

The total is more than half the 158 million who voted in the 2020 election, when President Joe Biden defeated Trump. It was a Democratic victory that to this day Trump says he was cheated out of by fraudulent voting rules and vote counts.

Dozens of court decisions, often rendered by Trump-appointed judges, went against him as he attempted to challenge the 2020 results. On Sunday, he told a Pennsylvania rally he "shouldn't have left" the White House in 2021 when Biden assumed office.

After he voted, Trump told reporters, "If it's a fair election, I'd be the first one to acknowledge" the results, though it was not clear what might meet that definition. Democratic critics say they expect Trump to challenge the outcome unless he wins.

A Trump victory would make him only the second president to serve two non-consecutive terms, after Grover Cleveland in the 1880s. He would also be the first felon to serve as president as he awaits sentencing later in November after being convicted of 34 charges linked to his hush money payment to a porn film star ahead of his successful 2016 run for the presidency.

Harris for weeks has claimed she is the underdog in the campaign but lately expressed more optimism and now says she expects to become the country's 47th president. If elected, she would be the first woman to be the American leader, its first of South Asian descent and its second Black president after Barack Obama.

Pollsters say the country's voters are deeply divided between the two candidates. It is an assessment reflected in how major media outlets look at the possible outcome.

Last-minute polling shows the Harris-Trump race all but tied in the battleground states.

The importance of the battleground states cannot be overstated.

U.S. presidential elections are not decided by the national popular vote but through the Electoral College, which turns the election into 50 state-by-state contests, with 48 states awarding all their electoral votes to the winner in those states. Nebraska and Maine allocate theirs by both statewide and congressional district vote counts.

The number of electoral votes in each state is based on population, so the biggest states hold the most sway in determining the overall national outcome, with the winner needing 270 of the 538 electoral votes to claim the presidency

Aside from the 19 electoral votes at stake in Pennsylvania, two other battleground states, Georgia and North Carolina, have 16 apiece, and Michigan has 15.

Polls show either Harris or Trump with substantial or somewhat comfortable leads in 43 of the states, enough for each to get to 200 electoral votes or more. Barring an upset in one of those states, the winner will be decided in the seven remaining battleground states.