AMNA NAWAZ: Welcome to the "News Hour."

Voters are heading to the polls in steady numbers in closely watched state contests, from governor's races in New Jersey and Virginia to the choice from mayor in New York.

GEOFF BENNETT: Today marks the first major Election Day since President Donald Trump's return to the White House, and his policies are proving to be a defining issue in races across the country.

Liz Landers reports on what the candidates and voters are saying as votes are cast and counted.

LIZ LANDERS: In New York City, candidates made a final push to sway voters heading to the polls.

ZOHRAN MAMDANI (D), New York City Mayoral Candidate: It is a day that we have been dreaming of for more than a year.

FMR.

GOV.

ANDREW CUOMO (I-NY), New York City Mayoral Candidate: We're still deciding.

(LAUGHTER) LIZ LANDERS: Democratic socialist Zohran Mamdani, the front-runner in the race to lead America's largest city, has energized some voters.

GREGORY JONES, New York City Voter: I'm very hopeful.

It feels -- I haven't felt this excited about an election since probably 2008, when Obama ran.

LIZ LANDERS: But others are worried his policies are too far left, uniting some of them behind former governor turned independent Andrew Cuomo.

BARBARA, New York City Voter: Not necessarily we like.

DANIELA BARBERA, New York City Voter: Right, exactly.

We had to live here through COVID, so we know how important it is to have representation of police in the street.

LIZ LANDERS: In an 11th-hour endorsement of Cuomo over the Republican, Curtis Sliwa, President Trump threatened to cut federal funds to his native city if Mamdani wins.

Even as Trump attempts to make inroads in blue states, Democrats out of power in Washington see gubernatorial races as a crucial counterweight.

Virginia will elect its first female governor, with voters choosing between Democrat Abigail Spanberger and Republican Winsome Earle-Sears in a state often seen as a national bellwether.

NATHAN, Virginia Voter: I definitely think it's a referendum on Donald Trump and just the direction the country's going in.

LIZ LANDERS: With many residents affected by the federal government shutdown, many voters say economy and education are what's driving their vote.

MARVINA COOPER, Virginia Voter: Food prices, gas prices, inflation, nothing is being done.

The crime, very interested in that.

And our children, our children are most important.

LIZ LANDERS: While, in New Jersey, Democrat Mikie Sherrill is trying to hold off a strong Republican challenger, Jack Ciattarelli, who came within striking distance four years ago.

Both gubernatorial candidates have focused on suburban counties, where high property taxes and cost of living dominate voters' concerns.

SAL RUIZ, New Jersey Voter: I think some people have legitimate concerns about the way the state is going and who's going to take the next steps.

And I do think that you'll see a split or people will split on those decisions.

FELIX ROSA, New Jersey Voter: Whatever Trump is doing, it's a little bit insane out there.

So most of people are just changing sides and voting against that.

LIZ LANDERS: Meanwhile, out West, California voters face a rare single-issue ballot fight, part of a larger national debate over redistricting, which could flip as many as five U.S.

House seats into Democratic control.

From coast to coast, last-minute campaigning, deep political divides, and a critical test for both parties ahead of next year's midterm elections.

For the "PBS News Hour," I'm Liz Landers.