After a decisive victory of Donald Trump in the South Carolina Republican primary, Marco Rubio and Ted Cruz both looked to cast themselves as the only candidate able to challenge the billionaire front-runner for the party's 2016 presidential nomination.

Rubio, who finished second in South Carolina, and Cruz, who came in at third just behind Rubio, noted that approximately 70 percent of Republicans don't support the former reality television show host, and said they could consolidate voters from that bloc, particularly now that Jeb Bush, the onetime front-runner and fundraising leader, has suspended his campaign.

"As this race continues to narrow, I think it’ll be easier and easier for that 70 percent to coalesce, and so that’s why I feel so good," Rubio, Florida's junior U.S. Senator, said on "Fox News Sunday." "I believe it’s literally down to three people who are running full-scale national campaigns."

Rubio, a member of the Senate foreign relations committee, told reporters on his campaign jet that U.S. presidents need to grasp world issues from their first day in office—and suggested that would be a stretch for Trump. "It's not about taking on Trump, but there are differences, and we are going to talk about them, particularly on foreign policy. Donald, now that the race has narrowed, needs to step up and outline his policy vision. And it can't be something that relies on experts he won't name." 

At rallies in Tennessee and Little Rock, Arkansas, the Floridian said his campaign will be focused on expanding the Republican message to include millions of working-class Americans he said haven't traditionally been among the party's base. In Franklin, a small town on the outskirts of Nashville, he drew more than 3,000 people and the equally impressive Little Rock crowd continued a trend that has seen his events swelling over the past two weeks compared to pre-New Hampshire levels. Both states are among a dozen scheduled to hold their Republican primaries on the March 1, the make-or-break day known as Super Tuesday. 

Late Sunday, Rubio headed to Summerlin, Nevada, and was slated to hold rallies in Reno, Elko and Douglas County on Monday.  

Rubio's aggressive schedule and sharpened lines of attack could be a taste of what is to come in a race quickly moving beyond the retail politics of the first three nominating contests and shifting more to one in which advertising and organization—and the money to do those things—are the determining factors.

Trump has resisted efforts to end his outsider candidacy, and shucked off criticism about changing positions on certain issues.  He's won the last two nominating contests—New Hampshire and South Carolina—by significant margins. The exit by Bush, an establishment favorite whose family has been on the last five winning Republican presidential tickets, released many of the top Republican donors, advisers, and endorsers he'd captured early on—a coalition that has long sought to end Trump's momentum but that also competed for votes with other Trump alternatives.

Rubio received the support of key South Carolina officials, including the popular Governor Nikki Haley, even before Bush dropped out, but said he has yet to win a nominating contest or do better than Trump—a point on which Cruz, winner of the Iowa caucus on Feb. 1, pounced. 

"We're seeing people come together behind our campaign because we are the only campaign that has beaten Donald Trump and that can beat Donald Trump," Cruz, a Texas senator, said on CBS's "Face the Nation." 

Cruz and Rubio also attacked one another, with Rubio saying Cruz was "very weak on national security" and "literally every day making up things." Cruz, who has said he is the only true conservative in the race, said Rubio's efforts to pass doomed immigration reform would hamper his ability to take on Trump, who has taken a hard line on immigration, and said his competitor had been "unwilling or afraid" to attack Trump.

"Donald devotes all of his time and energy, all of his money, to attacking me," Cruz said on ABC's "This Week With George Stephanopoulos." "That demonstrates that Donald sees me as the only real threat to him."

Trump seemed to acknowledge the nature of the three-candidate race when he praised both men for their acumen, even while defending his use of the same attack on Rubio that he's used against Cruz—that he is ineligible to serve as president. 

"I think the lawyers have to determine that," said Trump, who retweeted an accusation that neither man could serve as president. "I'm not sure. I mean, let people make their own determination."

Both Rubio and Cruz were born as American citizens. Cruz was born in Calgary, Canada, to a U.S. mother and a Cuban-born father. Rubio was born in the Miami to Cuban refugee parents. Trump said he was concerned "not so much with Marco."

There were wrinkles in the simple three-candidate narrative: Trump praised Ben Carson, the retired neurosurgeon who came in last in South Carolina. Rubio, meanwhile, downplayed the candidacy of Ohio Governor John Kasich, who has sought favor with some of the same establishment voters that Rubio and Bush have targeted.

"It’s clear that Kasich is going to focus entirely on Michigan," he said on Fox. "We’re going to continue to work everywhere."

Rubio also downplayed a report that Mitt Romney, the 2012 Republican presidential nominee and an establishment favorite, would be endorsing him.  "I would love to have his endorsement but there's nothing forthcoming today and—or in the days to come as far as I know," Rubio said on ABC.

I'n an e-mail memo to supporters on Sunday, Rubio campaign manager Terry Sullivan said the results in South Carolina showed the strength of Rubio as a candidate and of his message.

"The results show that Marco was heard loud and clear by South Carolinians," he wrote.

In the memo, Sullivan tried to cast doubt on Cruz's electability, noting that more than 7 in 10 South Carolina voters identify as evangelical, a base that should have delivered for the Texas senator. 

As of now, all six candidates will compete in the Nevada Republican caucus on Feb. 23. 

On the Democratic side, Hillary Clinton and Bernie Sanders battled over the meaning of the results of Saturday's Nevada caucuses, which Clinton won.

Sanders, a Vermont senator and self-described democratic socialist who now must prove he can stop Clinton, sought to portray himself as the candidate of young people, the economically disaffected, and even some minority groups. Sanders said that he had won the Latino vote in Nevada, which he called "a huge way forward for us." That assessment was based on entrance polling. Clinton said on the same program her campaign did not think those polls were "particularly accurate."

A Clinton spokesman had tweeted Saturday night that "in Nevada's Latino-majority precincts, Clinton won 207 delegates and Sanders won just 130. Proves entrance polls were wrong."

Clinton said she had work to do with independents, as well skeptical voters, saying "an underlying question that maybe is really in the back of people's minds, and that is, you know, is she in it for us or is she in it for herself?"

The two face off next in South Carolina on Feb. 27, the first Southern nominating contest for the Democrats this year.  The Democratic electorate there is heavily African-American, a group that Clinton won by a wide margin in Nevada and which Sanders said he hopes to win over with his message on criminal justice and the economy. 

Before it's here, it's on the Bloomberg Terminal. LEARN MORE