MANCHESTER, N.H. | President Trump cruised to an easy victory Tuesday night in New Hampshire’s first-in-the-nation Republican presidential primary, counting on the strong showing to turn the state red in November.

The president blew past “Never Trump” resistance from former Massachusetts Gov. Bill Weld, who said it was important to show voters they had an alternative. The Associated Press declared Mr. Trump the winner shortly after polls closed at 8 p.m.; the president had about 85% of the vote with more than half of precincts reporting.

Mr. Weld was banking most of his long-shot hopes on a strong performance in his backyard, and the lopsided loss could hasten his withdrawal from the race.

As the campaigns move to South Carolina, Nevada and 14 Super Tuesday states, Mr. Trump and his allies were assessing the looming impact of former New York City Mayor Michael R. Bloomberg, who wasn’t on the ballot in New Hampshire or Iowa but has been rising in polls.

“If you’ve got $60 billion, you can tell your own story. I think he’ll be a force to be reckoned with,” said Sen. Lindsey Graham, South Carolina Republican, on SiriusXM. “But the problem is, I don’t know if the Bernie [Bernard Sanders] people would tolerate a Bloomberg.”

While the Democrats try to sort out a crowded field without a clear front-runner, the president has been showing his popularity and organizational muscle in early voting states. He sparked record turnout for an incumbent in Iowa.

The turnout in New Hampshire also appeared to be setting records. Trump campaign manager Brad Parscale said with about 54% of precincts reporting, Mr. Trump had already received more votes than Presidents Barack Obama (49,080), George W. Bush (52,962) and Ronald Reagan (65,033) in the New Hampshire primaries for their uncontested reelection campaigns.

He also drew a packed arena of about 11,000 supporters and an overflow crowd on Monday night at Southern New Hampshire University in Manchester, a larger audience than any of the Democratic candidates could muster. Some in the crowd showed up 35 hours ahead of time for the rally.

Campaign officials said about 25% of those attending the Trump rally were registered Democrats, and Mr. Parscale said half of the rally attendees from New Hampshire hadn’t voted at all in 2016.

“Those numbers alone take us over the winning line,” he told Fox News.

The Trump reelection campaign deployed dozens of high-profile supporters such as American Conservative Union Chairman Matt Schlapp, members of the president’s family and staff on primary day. Republican Gov. Chris Sununu predicted the momentum will enable Mr. Trump to win the state in November, after losing it in 2016 to Democratic presidential nominee Hillary Clinton by fewer than 3,000 votes.

New Hampshire resident Greg Danas, 56, owner of a forensic lab, voted for Mr. Trump on Tuesday and believes the president will capture the state because of the strong economy.

“I think New Hampshire is probably going to go Republican this year,” Mr. Danas said. “For the sake of people’s well-being financially — everyone votes their pocketbook normally. I think Trump is going to take … 45 states just because of the economy. He’ll get a lot of swing states — he’ll take New Hampshire easily.”

But lifelong Republican Emalou Abbot, 85, of Milford, changed party affiliation recently and said she is “not fond” of Mr. Trump. She voted for Democrat Tom Steyer.

“I’m a born Republican,” she said. “Maybe this year’s a good year to stay out of the Republican Party so I won’t have to vote for Trump. This is an awful thing, but I don’t mind saying it to you: when they get Trump out of there, I’ll be glad to go back.”

⦁ Dave Boyer reported from Washington.

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