DES MOINES — Two days after their confrontation in Thursday night's debate, Sen. Marco Rubio and Gov. Chris Christie continued to duke it out for 2016 supremacy as both spent their Saturday courting potential caucus-goers in Iowa.

The two, who mixed it up after a week-long back-and-forth after attacks from Rubio's super political action committee (Conservative Solutions PAC), each used rehearsed broadsides against each other with only 15 days until the first-in-the-nation caucus.

Sitting in the third spot behind Sen. Ted Cruz and Donald Trump, Rubio has kept up his recent lines of attack against the New Jersey governor, hitting him over past stances on Common Core and gun control, as well as Christie's 2009 support for confirming Sonia Sotomayor to the Supreme Court. Christie disputes taking those positions.

"There's some policy differences between us," Rubio told a standing-room crowd in Johnston. "He supported Common Core, he supports gun control ... and one of the things he supported was Sonia Sotomayor for the Supreme Court. I would never support something like that."

Rubio noted the next president could have up to four Supreme Court nominations to make. He said he'd nominate judges like Antonin Scalia and Clarence Thomas.

"I should have brought it with me — I actually have Chris Christie's press release with the letter head on it saying he supports Sotomayor's confirmation not once, but twice. That's a fact," Rubio told reporters afterwards. "He supported Common Core. That's a fact."

While Rubio would like to gain on Cruz and Trump, who have assumed nearly all authority in Iowa since November after the fall of Dr. Ben Carson, equally important is holding the New Jersey governor at bay in Iowa before the New Hampshire primary, where Christie is betting on success.

Since receiving the endorsement of the newspaper the Union Leader in late November, Christie has edged into the top give in the Granite State with 9.2 percent, according to the latest RealClearPolitics. He has been unable to catch Rubio, who lags well behind Trump.

Christie touts his executive experience in a bid to distinguish himself from rivals.

"I'd like to do as well as I can, but I've said all along my initial goal in this was to be the No. 1 governor," Christie told reporters after yet another marathon town hall in Fort Dodge. "If I can be the No. 1 governor coming out of here, I feel I'll have had a pretty good night."

"There's a difference between having run something before and not having run something before. This is not a new argument for me," Christie said. "The fact is, we tried a first-term senator who never ran a thing in their lives [sic] before, and I don't think that by changing that person's philosophy politically that that's going to make that person more competent to run the government."

In the process, Christie took a shot at Rubio, who's cited Senate dysfunction as the reason he is not seeking re-election in November. Last week, Rubio told a Cedar Rapids crowd that members of Congress cannot set the agenda in Washington.

Christie has jumped on those remarks.

"Marco was elected in 2010. He spent a good part of the last year or two not being in the Senate, bragging about not going to the Senate 'cause he says it's worthless, it's not interesting," Christie said. "I also agree with Marco when he said a week ago or so that senators or congressmen can't fix America's problems."

Pitfalls await Christie in Iowa. Besides his continued battle with Rubio, Christie is looking to top Carson and former Florida Gov. Jeb Bush.

"It's time," Christie said when asked what his biggest challenge is over the next two weeks. "You want to meet as many people as you can. If you guys talked to any of those folks in there tonight, we came out with a lot of converts tonight. But it's time and it's 12 different candidates for them to have to choose from and get through all the commercials and the mailers and all the rest of it. So just a matter of trying to differentiate yourself."

Christie is set to hold three events in the state on Sunday, with Rubio back in the state on Monday for five of his own.Rubio is third in the Washington Examiner's presidential power rankings, while Christie is fourth.