Trump wins, but the contest for the Republican nomination rolls on | McClatchy Washington Bureau

Donald Trump notched a big first political win this primary season, but the race for a Republican establishment alternative remains muddled, setting the Republican party up for a grueling fight to the presidential nomination.

The brash real estate magnate easily won the New Hampshire vote, with Ohio Gov. John Kasich placing a solid second. Iowa winner Sen. Ted Cruz, who wasn’t considered a natural fit for the state, courted the conservative and tea party vote and finished third, with a narrow margin over former Florida Gov. Jeb Bush who claimed fourth with a slim lead margin over Sen. Marco Rubio.

The results suggest that Trump is improving his political skills and emerging as a more serious political threat to the Republican mainline.

With Sen. Marco Rubio, who claimed victory after a surprise third-place finish in Iowa, wilting after a disastrous debate on Saturday, there is no consensus establishment candidate – giving Trump more time to strengthen his case as his rivals continue to snipe at one another.

Trump won in his familiar blunt way, promising at giant rallies to “make America great again” and launching assaults against the “stupid people” who he says run the government. Exit polls show he attracted huge numbers of voters unhappy with their government and the direction of the country.

But Trump learned important lessons from his first political loss in Iowa where he skipped a presidential debate and staged massive gatherings, rather than engaging voters one-on-one.

In New Hampshire, where tradition holds that voters want to meet the candidates at least twice before making up their minds, Trump stepped it up in the closing days. He met with small business owners, shook hands with a breakfast crowd at a diner and fielded questions from voters at the kind of intimate town hall his rivals had held for months. He visited a polling station on primary day, and dispatched his daughter, Ivanka, to shake hands with voters.

“You started it, remember. You started it,” a victorious Trump told his New Hampshire supporters.

In perhaps a bid to quell fears about his temperament, he mostly shied away from personal attacks on his rivals as they debated Saturday. But he proved unable to entirely stop himself, chortling Monday night as he repeated a supporter’s denunciation of Cruz as a “pussy.”

On Tuesday, however, he suggested a President Trump would be more buttoned up: “If you’re about to be president, you would act differently,” he told NBC News.

The brashness, though, is what his voters like. Exit polls showed 57 percent of voters wanted someone outside the political establishment.

“He’s not a politician,” said voter Cindi Tuite of Kingston, New Hampshire, adding that Trump has guts. “No one else is saying it like he is.”

The night’s other winner was Kasich, who finished in second place, giving him an opportunity to claim the establishment mantle. Kasich had staked most of his presidential ambitions on New Hampshire, holding more than 100 town halls across the state and racking up endorsements from more newspaper editorial boards in the state than any of his rivals.

But the electoral math in some of the upcoming Southern states may be complicated for Kasich, who has touted himself as a center-right alternative to the party’s more conservative candidates.

“I’m the right porridge,” Kasich said when a woman at a town hall told him she was trying to decide among him, Hillary Clinton and Bernie Sanders. “One of them is too hot, one of them is too cold.”

Cruz, the surprise Iowa winner, with a deep appeal to evangelical voters, wasn’t seen as a natural fit for flinty New Hampshire. But he campaigned aggressively, pitching himself as the only true conservative in the race.

The calendar, at least for the next month, can keep Cruz in the running, with contests that include the sort of evangelicals and hard-core conservatives who gave him the lift in Iowa.

Many conservatives who like Cruz and Rubio but lean toward Rubio because he is considered “more electable,” may move to Cruz when the campaigns shift South, suggested conservative strategist Greg Mueller.

New Jersey Gov. Chris Christie also bet on New Hampshire for his breakout moment, but though he was the one to eviscerate Rubio on the debate stage, he failed to grab much traction, with perhaps Trump siphoning many discontented voters who might otherwise been drawn to Christie’s combativeness.

Christie, though was finishing with less than 10 percent of the vote and said he’d head back to New Jersey to reconsider the race.

The biggest loser was Rubio.

Rubio rode a wave of momentum into New Hampshire from a surprisingly strong third-place finish in Iowa that he seized as victory. But that wave crested at Saturday’s debate, when he four times recited word-for-word the same line of attack against Obama – playing into criticism that he’s too scripted.

A clearly disappointed Rubio took the blame for the showing Tuesday, promising supporters it would not happen again. That ups the ante for him going into this Saturday’s debate in Greenville, South Carolina.

The state, where more than 60 percent of Republican voters are evangelicals, votes Feb. 20, followed by Nevada three days later, where religious Republicans dominate. Next up are 11 Southern and Midwestern states March 1 and 5 with sizable numbers of Christian voters.

South Carolina’s “first in the South” primary has an establishment-friendly electorate, but Trump has remained atop the polls since last September, with a wide lead over second-place Cruz and third-place Rubio.

Trump has visits planned to the state, and former Alaska Gov. Sarah Palin, who endorsed him over Cruz but did not show up in New Hampshire, told CNN she plans to campaign for Trump in South Carolina.

New Hampshire also provided a ticket for Jeb Bush, who has campaigned across the state relentlessly and has waged an aggressive fight with Trump, questioning his conservative bona fides.

“This campaign is not dead. We’re going on to South Carolina,” Bush told supporters, as the cable networks switched to Trump’s victory speech.

Heading South, Bush has the benefit of a massive campaign chest, a well-funded super PAC and the support of much of the South Carolina Republican establishment. That includes native son Sen. Lindsey Graham, who endorsed Bush after ending his own bid for the nomination.

The state has favored the Bush family in the past: George H.W. Bush won South Carolina in 1988, after placing third in Iowa and first in New Hampshire, and George W. Bush, who appears in a South Carolina TV ad for his brother and will likely campaign for him there ahead of the Feb. 20 primary, won the state in 2000 – after winning Iowa and placing second in New Hampshire.

Jeb Bush, Kasich and Rubio, if they stay in the contest, might face a lift in later rounds: Michigan votes March 8, followed by Missouri, Illinois, Ohio, Florida and other states a week later. The religious right has less clout in those states, which have long been kinder to center-right Republicans.