WASHINGTON (CNN) -- Former Massachusetts Gov. Mitt Romney dismissed Sen. John McCain's, R-Arizona, sharp critique Tuesday, and reiterated his opposition to the immigration deal in Congress.

"I have respect for Sen. McCain," Romney told reporters at an event in Dallas, Texas. "That shows you that even when he is wrong, he is amusing.

Romney is a sharp critic of the Senate immigration measure -- backed by McCain -- that calls in part for putting illegal immigrants currently residing in the United States on a path to citizenship.

Romney's remarks come one day after McCain joked that that the former Massachusetts governor's solution to the immigration problem might be "to get out his small varmint gun and drive those Guatemalans off his lawn."

McCain, alluding to criticisms that Romney changes position depending on what is politically expedient, also that he'd "wait a couple of weeks and see if the winds change and Mitt comes back around."

On Tuesday, Romney brushed aside McCain's suggestion that his immigration stance had shifted, saying "I am best off to describe my positions."

"I would like us to secure the border," he added. "I would like us to have an employment verification system so we know who is here legally and able to work and who is not. I would also like to make sure for the 12 million who are here illegally today that while they have an opportunity to apply for citizenship and permanent residency that they don't get any advantage in them coming here illegally."

Also in Texas Tuesday, McCain challenged critics of the Senate measure to put forth another proposal that has a chance of passing in the highly-divided Congress.

"I think it's a matter of national security, and to do nothing -- to leave the status quo -- would be an abrogation of our responsibilities to the American people," he said at a campaign event in Houston. "If they've got another proposal that will pass the Congress of the United States, then let's hear that."