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Bloomberg threat has candidates' attention on both sides

New York Mayor Michael Bloomberg pauses after speaking to the Economic Club of New York in what is being billed as his last major speech as Mayor of New York City on December 18, 2013 in New York City.

Spencer Platt, Getty Images

Hillary Clinton doesn't believe former New York City Mayor Michael Bloomberg will need to jump into the presidential race any time soon.

"The way I read what he said is if I didn't get the nomination he might consider it," Clinton told NBC News Sunday, referring to the reason behind Bloomberg considering an independent bid. "Well, I'm going to relieve him of that and get the nomination so he doesn't have to."

Sources familiar with Bloomberg's thinking told CBS News on Saturday that the billionaire New Yorker would likely run if Clinton was defeated in the Democratic primary and the eventual GOP nominee was either Donald Trump or Ted Cruz. The possibility that the extremes of either party were to win, one close adviser told CBS, "has [Bloomberg] thinking seriously about this."

The businessman, who Clinton called a "good friend" during her interview, will make a final decision by early March after the first nominating contests in Iowa, New Hampshire, and South Carolina.

Until that time, however, the former secretary of state said that she would simply observe what unfolds with the current race.

"I'm going to do the best I can to make sure that I get the nomination," Clinton said. "And we'll go from there."

Some Republicans also went with a wait-and-see strategy when it comes to Bloomberg entering the race.

On Fox News Sunday, Florida Sen. Marco Rubio said that "If he becomes a candidate, then we'll have a conversation about our differences."

"If he was just out there talking about running for president," Rubio went on, "well, there's a lot of people that have done that."

"As of now, he's just a private citizen who owns a big company," he added.

In an interview with CNN, New Jersey Gov. Chris Christie commented that "no one can be evaluated about whether they would be a good president or not until they get into the race."

"When you're not a candidate, you don't deserve to be evaluated as whether you're going to be a good president or not," Christie said.

Former Florida Gov. Jeb Bush weighed in on Bloomberg's flirtation with a presidential bid.

"Mike Bloomberg is a good man," Bush told CNN. "We disagree on a whole lot of things, but he's a good person and he's a patriot. And he wants the best for the country. But we have differing views."

One candidate, however, relished the challenge Bloomberg could present if he were to enter the 2016 contest.

"I'd love to compete against Michael," GOP front-runner and fellow New York businessman Donald Trump said on CBS' "Face the Nation." "I know him very well. And I think he might very well get in the race and I would love to have him get in the race."