Former New York City mayor Michael Bloomberg. REUTERS/Stephane Mahe/Files

On the Sunday morning talk shows, there was one thing most of the presidential candidates agreed on: Former New York mayor Michael Bloomberg, relatively frequent flirter with the idea of a third-party presidential bid, is not a problem for them. No problem at all.

[Michael Bloomberg considers a presidential run]

In fact, some went a step further and all but said, 'bring it."

Here was the exchange between Sen. Bernie Sanders, an independent from Vermont seeking the Democratic Party's presidential nomination, and ABC's Martha Raddatz on, "This Week,":

RADDATZ: And what do you think about the possibility of former Mayor Michael Bloomberg, another billionaire, getting in the race?

SANDERS: Well, you know, I think it would be very interesting if Donald Trump became the Republican candidate who is a multi-billionaire, and Michael Bloomberg became an independent candidate who is a multi-billionaire. And it will tell people what I have been saying for a long time is that this country is moving away from democracy to oligarchy that billionaires are the people who are controlling our political life. That is what -- that is not what, to my view, American democracy is supposed to be about, a contest between billionaires. If that takes place, I am confident that we will win it.

Here's the key part of what happened when CBS's John Dickerson asked Donald Trump, GOP presidential contender, about Bloomberg on "Face the Nation,":

DICKERSON: Let me ask you somebody else who is thinking about getting in the race, Michael Bloomberg. You said yesterday, "I love it" if he -- speaking about him getting in the race. Why would you love it?

TRUMP: Well, I would love it. I know Michael very well. I would love to compete against Michael. And 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....He's very opposite on me with guns, and he's opposite on pro-life, and he's opposite on lot of things. So, I would love to have Michael get in the race. But I don't know if he's going to do it. But I hope he does. I would love to compete against Michael.

DICKERSON: One of the reasons he would get in the race, he's thinking, is because you're doing so well. It would be to counterbalance you.

TRUMP: Well, that would be good. That's a good thing. I would love to have Michael get in the race. And Michael has been a friend of mine over the years. Perhaps we're not friends anymore. He's wanted to do this for a long time. And he never pulled the trigger, and we will see if he does right now. But I would personally love to compete with Michael Bloomberg.

A question about a Bloomberg third-party run put to Sen. Marco Rubio by "Fox News Sunday" host Chris Wallace brought on this exchange and some very familiar language:

WALLACE: Senator, we're running out of the time, so I'm going to ask you for a quick reaction. As I'm sure you have seen there's news stories today, "The New York Times" reporting that billionaire and former New York City Mayor Michael Bloomberg is considering a third- party run for president. How would he shake up the race?

RUBIO: Well, I don't -- I haven't spent time thinking about Mayor Bloomberg or what he might or might not do. I've met him a couple times, don't know him well, don't agree with his stance on the Second Amendment and some other issues. I'll wait until he becomes a candidate. If he becomes a candidate, then we'll have a conversation about our differences. If he as just out there talking about running for president, well, there's a lots of people that have done that. So, as of now, he's just a private citizen who owns a big company. If he decides to become a candidate, we'll engage in a debate at that time.

WALLACE: Do you feel at a disadvantage when you've got Bloomberg and Trump who are both billionaires?

RUBIO: I think this is a great country where the son of a bartender and maid can be running for the same office and have the same opportunity as the son of a millionaire or for that matter the son of a president. It's extraordinary. No other country in the world would that be possible.That's why I'm running. I want America to remain that kind of country.

And, Jeb Bush pretty much said the same when CNN's Jake Tapper questioned him about Bloomberg on "State of the Union,":

TAPPER: Former New York City Mayor Mike Bloomberg has instructed advisers to draw up plans for a potential independent run for president. He's reportedly troubled by the prospect of Bernie Sanders being the Democratic nominee and either Trump or Cruz being the Republican nominee. If we get to the general election and, God forbid, you didn't win the nomination, and you had the choice of Trump, Bloomberg, Sanders, would you consider getting behind the former New York City mayor?

BUSH: You know what? That's not going to happen. The party process is going to work far differently than what the pundits are saying. I totally believe that. Mike Bloomberg is a good man. 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. And I want to be the conservative candidate to run -- to lead the conservative party into the general election. That's my focus.

When news that Bloomberg was considering a run broke this weekend, few long-time political reporters were willing to dismiss its importance. It would be, as The Washington Post's Karen Tumulty put it Saturday, "a move that could provide yet another wild turn in a 2016 race that has already seen more than its share of them."

Most Americans are at least somewhat suspicious about the effect that third-party runs launched by H.Ross Perot in 1992 and Ralph Nader in 2000 had on each election outcome. In 1996, Perot pulled in nearly 20 percent of the vote, although it has never been clear that a disproportionate share came from what might have been then President George H.W. Bush's supporters. However, Bush did become an incumbent candidate who lost the race to then-Gov. Bill Clinton. Nader's impact on the 2000 election was far smaller, pulling in under 3 percent of the vote. But that, as you will recall, was an extremely close race between George W. Bush and Al Gore.