"I would love to take on Ted one-on-one, I think that would be so much fun," Trump said Monday.
In a new ad, Trump portrays Rubio as desperate and unfit for office.
"Rubio's been a total no-show in the U.S. Senate, with the worst voting record of all," the ad says.
Cruz contends the Trump bubble is beginning to burst.
"If you want to beat him, you got to beat him at the ballot box. And our campaign is the only campaign that has demonstrated we can do so over and over," he said on the campaign trail.
Cruz is working to line up several Republican Senate endorsements, an ironic twist for a candidate who has also run an anti-establishment campaign.
Outside groups are also lining up against Trump, unveiling a slew of new negative commercials. The ads attack Trump for using vulgarities, his description of Vietnam POW John McCain as a loser, and on his past liberal policy positions.
"Which candidate supports higher taxes, national health care and the Wall Street bailout? It's Donald Trump," one ad says.
On Monday, Trump warned thousands of supporters in North Carolina it's only just begun.
"Do you see the money they spend? See the millions in negative ads about me that are mostly phony ads?" Trump asked the crowd.
The latest poll in Michigan, which votes tomorrow, shows Trump with a 14-point lead on Cruz. Trump wants a big win to bolster his claim that a populist message can help the GOP win Rust Belt states in a general election.