More than 240,000 new Democrats and independents showed up to vote in Virginia’s Republican presidential primary this week — the tip of a massive shift as all the enthusiasm and interest are moving to the GOP.

The numbers are staggering in other big states as well: More than 535,000 new Democrats and independents in Texas, 175,000 in Georgia, 172,000 in Tennessee and 143,000 in Alabama, according to a Washington Times analysis of exit polling that compared this year’s election with the 2008 race, the last time both parties had a contested primary.

Donald Trump, the iconoclastic Republican front-runner, says it’s all his doing.

“We have expanded the Republican Party,” the billionaire businessman declared Tuesday night, as results showed Republicans demolishing record after record in primary turnout. “They’re longtime Democrats and they were never going to switch, and they all switched. And they were independents. And we’ve actually expanded the party.”

Exit polling shows Mr. Trump has indeed helped build up the party this year, with nearly 10 million people casting ballots in the 15 primaries and caucuses so far, about 4 million more than voted in the same Republican races in 2008.

Mr. Trump has won about a third of the votes, building a formidable and durable coalition that somehow spans moderates and evangelicals, draws heavily from self-identified independents, and tilts toward older and less-educated supporters.

Just how successful he and his fellow candidates have been is captured in the numbers: 14 of the 15 Republican contests so far have set records for turnout.

Just as striking is the drop-off for Democrats who, though setting a record Tuesday in Colorado’s caucuses, have seen turnout plummet in every other race. Accounting for all 15 races so far, Democratic turnout is down more than 30 percent compared with the heady days of 2008, when Barack Obama battled Hillary Clinton in an epic clash.

In fact, the numbers this year are almost exactly reversed. Through the same races in 2008, Democrats had accounted for 62 percent of all votes cast. But this year, powered by a surge of interest from Democrats, Republicans and independents alike, Republicans account for 59 percent of the votes cast.

Democrats insist much of the difference is attributable to the size of the Republican field, which went into Iowa with a dozen candidates, compared with three for Democrats. In Super Tuesday races, Republicans had five candidates and Democrats were down to two: Mrs. Clinton and Sen. Bernard Sanders.

“I understand there’s been a disparity across the country. I think it’s a disparity that’s caused by the fact that the Republicans have so many candidates,” Sen. Amy Klobuchar, Minnesota Democrat, told MSNBC’s “Andrea Mitchell Reports” program. “They’ve had a major, major race. We’ve had one too, and it’s really important, but it’s not been nearly as volatile.”

The White House saw the math the other way. Press secretary Josh Earnest said that when the votes were tallied in states such as Virginia, Mrs. Clinton ended up with more support in her two-person race than any of the five Republican candidates did.

“I think this is an indication that there is ample enthusiasm on the Democratic side, particularly in the places where it matters most in the general election,” Mr. Earnest said.

Indeed, most of the races Tuesday were in states that are unlikely to be battlegrounds in November’s general election. Virginia was the chief exception.

Digging into the numbers, though, Republicans said they are confident that the overall turnout in Virginia bodes well for recapturing the state in November. Mr. Obama won Virginia in 2008 and 2012.

“Nearly 240,000 more voters chose to cast a ballot for Republican candidates versus Hillary or Bernie,” said John Findlay, executive director of the Virginia Republican Party.

Mr. Findlay said Republican turnout exceeded that of Democrats in almost every region of the state, including the big suburban swing counties of Loudoun and Prince William in the Washington region, Henrico, on the outskirts of Richmond, and Chesapeake, in the southeast.

“The road to the White House runs through these localities — and Republican candidates had more votes on Tuesday than Democrats in each and every one of them,” he said.

Mr. Earnest said some of the massive Republican turnout is “due to hostility” toward Mr. Trump, suggesting he could be a drag on the party if he is the nominee in November.

A number of voters emerging from polling places Tuesday said they were searching for an anti-Trump strategy. That was the case for Cori DeFrancis, 61, a consignment shop owner voting in Atlanta who backed Sen. Marco Rubio in the Republican primary because she thought he had the best chance of beating Mr. Trump.

“I’m very, very concerned about Donald Trump becoming the nominee,” she said. “I find him embarrassing to our party.”

Party leaders are also worried that Mr. Trump will drive away rank-and-file Republicans like Ms. DeFrancis.

Mr. Trump, though, says the numbers speak for themselves.

“We’re going to be a unified party,” he said. “And we are going to be a much bigger party, and you can see that happening. We’re going to be a much bigger party. Our party is expanding. And all you have to do it take a look at the primary states where I’ve won.”

His coalition hits the Republican sweet spot. He does best among voters who identify as “somewhat conservative” while holding his own among very conservative and moderate voters.

It’s also striking which demographics are not trouncing Mr. Trump.

Analysts predicted that Hispanic voters would reject him for his brash comments about Mexico and his strong stance against illegal immigration, but in states with sizable Hispanic populations — Nevada and Texas — he has won Hispanic voters at nearly the same rate as his overall vote total.

• S.A. Miller, reporting in Atlanta, contributed to this report.

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