Republicans stumbled on Super Tuesday in their search for a standard-bearer to lead conservatives against interloper Donald Trump, who is poised to capture the party's presidential nomination.

Trump maintained his status as front-runner, bringing him closer to the March 15 primaries that could make his victory inevitable.

Some Republicans are mobilized in a #nevertrump Twitter campaign against the man nicknamed "The Donald," a political neophyte known primarily as a reality television star and gauche billionaire who mostly associated with Democrats until a few years ago.

Marco Rubio seemed to have been anointed as the party establishment's consensus candidate after finishing a close third in the February 1 Iowa caucus. But the Florida senator's breakthrough was undermined by mediocre results in the weeks that followed.

The son of Cuban refugees, the telegenic 44-year-old has forged a relatively optimistic message among a conservative field obsessed with bashing Democratic President Barack Obama. But Rubio's performance has been less than the sum of his politically advantageous parts.

He looked to be again failing to deliver on Super Tuesday, until, at last, scoring his first victory after 15 state contests in Minnesota.

Rubio's rival for the anti-Trump mantle, fellow Senator Ted Cruz, won Iowa a month ago and scored important victories Tuesday in his home state of Texas and neighbouring Oklahoma.

"So long as the field remains divided, Donald Trump's path to the nomination remains more likely, and that would be a disaster for Republicans, for conservatives and for the nation," Cruz said at a Texas rally.

He urged the other remaining candidates - Ohio Governor John Kasich and conservative activist Ben Carson - to cede the race to him: "Head to head, our campaign beats Donald Trump resoundingly. But for that to happen, we must come together."

Rubio, though, touted his strong second-place finish in Virginia - less than 3 points behind Trump's 35 per cent - and surge in support since a feisty debate performance last week.

"Five days ago, we began to explain to the American people that Donald Trump is a con artist," Rubio said, in a rally Tuesday in his home state of Florida. "We are seeing in state after state, his numbers going down and our numbers coming up."

Accusing the billionaire of appealing to intolerance, Rubio warned that nominating Trump would be the death of the modern Republican party.

Rubio is now looking ahead to contests Friday in Kansas, Kentucky, Louisiana and Maine, followed by Hawaii, Idaho, Michigan and Mississippi on March 8. All those are preludes to the March 15 primaries, when several populous states - most importantly his own Florida - will vote.

In particular, Florida and Ohio on that day will award their large delegate slates by winner-take-all method.

Kasich, who is considered popular in his home state of Ohio, hopes to make his own splash on March 15, though the party establishment is increasingly eager for him to get out of the race. In Virginia and Vermont, Rubio and Kasich together had enough votes to have easily toppled what became Trump victories.

Voter surveys within the last two weeks have shown Rubio trailing Trump in Florida by at least 16 percentage points, according to the website Real Clear Politics. If Trump continues leading the race and wins key states on March 15, he will be on a likely unstoppable path to the Republican nomination.

US Senator Lindsey Graham, who was once part of the 17-candidate Republican presidential field before quitting the race in December, long before the first votes were cast, described Trump on Tuesday as a "demagogue" who will lead the conservative party to defeat.

Graham told broadcaster CBS News that Rubio and Kasich will be finished if they fail to win their home states, and he made no secret of his own dislike for the brash Cruz, who is infamously unpopular among his fellow Republican senators.

Asked by the television interviewer if he would urge Republicans to rally around Cruz, if necessary, to stop Trump, Graham replied: "I can't believe I would say yes - but yes."

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