LANSING, Mich. — Donald Trump’s easy victories in Michigan, Mississippi and Hawaii left his rivals with shrinking opportunities to slow his momentum in the Republican primaries and little indication that a flurry of intense efforts to undermine his credibility are pushing voters away from the brash billionaire.
Democrat Bernie Sanders surprised front-runner Hillary Clinton in Michigan, a victory that breathed new life into his White House bid and forecast a long Democratic contest. But Clinton, who won Mississippi, padded her delegate lead and is now halfway to the number needed to clinch the nomination.
Clinton glossed over her contest with Sanders as she addressed supporters, choosing instead to focus her attention on Republicans and the general election.
‘‘We are better than what we are being offered by the Republicans,’’ she declared.
Trump entered Tuesday’s contests facing questions about his durability and ended the night with a pair of convincing victories. US Senator Ted Cruz of Texas added a win in Idaho, bolstering his case that he’s the only candidate who can beat Trump with some regularity.
US Senator Marco Rubio of Florida suffered another brutal drubbing, failing to pick up any delegates in Michigan and Mississippi. He faces a sudden-death contest in Florida next week. Similarly, Governor John Kasich of Ohio desperately needs to win his home state Tuesday to stay in the race.
With the prospect of a Trump nomination growing more likely, rival campaigns and outside groups have significantly stepped up efforts to discredit the real estate mogul. But the flood of attacks on Trump’s business record and temperament has failed to slow his rise.
‘‘Every single person who has attacked me has gone down,’’ Trump said at one of his Florida resorts. He was flanked by tables packed with his retail products, including steaks, bottled water and wine, and defended his business record more thoroughly than he outlined his policy proposals for the country.
While a handful of recent losses to Cruz have raised questions about Trump’s standing, Tuesday’s contests marked another lost opportunity for rivals desperate to stop his march to the nomination. Next week’s winner-take-all contests in Ohio and Florida loom as perhaps the last chance to block him short of a contested convention fight.
Kasich finished third in Michigan, behind Trump and Cruz. It wasn’t the boost he was looking for heading into next week’s crucial contest in his home state.
Rubio, whose appeal with party leaders hasn’t been reciprocated by voters, insisted he would press on to Florida.
‘‘It has to happen here, and it has to happen now,’’ Rubio told supporters at a Sarasota rally.
If Rubio and Kasich can’t win at home, the GOP primary appears set to become a two-person race between Trump and Cruz. The Texas senator is sticking close in the delegate count, and with seven states in his win column he’s argued he’s the only candidate standing between Trump and the GOP nomination.
During a campaign stop at a North Carolina church, Cruz took on Trump for asking rally attendees to pledge their allegiance to him. Cruz said the move struck him as ‘‘profoundly wrong’’ and was something ‘‘kings and queens demand’’ of their subjects.
Some mainstream Republicans have cast both Trump and Cruz as unelectable in a November faceoff with the Democratic nominee. But they’re quickly running out of options — and candidates —to prevent one of the men from becoming the GOP standard-bearer.
Trump also prevailed Tuesday in Hawaii’s Republican caucuses.
The economy ranked high on the list of concerns for voters in Michigan and Mississippi. At least 8 in 10 in each party’s primary said they were worried about where the American economy is heading, according to exit polls conducted by Edison Research for the Associated Press and television networks.
Among Democrats, 8 in 10 voters in both states said the country’s economic system benefits the wealthy, not all Americans.
Sanders has sought to tap into that concern, energizing young people and white, blue-collar voters with his calls for breaking up Wall Street banks and making tuition free at public colleges and universities. Michigan, with big college towns and a sizable population of working-class voters, was a good fit for him, though something of a surprise victory given that Clinton had led in polls heading into Tuesday’s voting.
Sanders has struggled mightily with black voters who are crucial to Democrats in the general election. In Mississippi, black voters comprised about two-thirds of the Democratic electorate and nearly 9 in 10 backed Clinton.
After Tuesday’s results, Clinton has accumulated 1,221 delegates and Sanders 571, including superdelegates. Democrats need 2,383 delegates to win the nomination.
Among Republicans, Trump has at least 446 and Cruz has at least 347. Rubio has at least 151 delegates and Kasich has at least 54. It takes 1,237 delegates to win the GOP nomination.
Pace reported from Washington. Associated Press writers Steve Peoples, Catherine Lucey, Sergio Bustos, Kathleen Ronayne, and Hope Yen contributed to this report.