Washington — Republican Sen. Marco Rubio of Florida hit back Thursday at the notion that his upcoming trip to headline a birthday fundraiser for Iowa’s governor, Terry Branstad, may be a move to lay some groundwork for a potential presidential run.

Rubio said “the trip to Iowa has nothing to do with 2016,” adding that he accepted the invitation before GOP nominee Mitt Romney lost the presidential election.

The speaking gig quickly stirred talk of a future White House bid for Rubio, as the event provides the freshman senator the chance to mingle with the Republican class in Iowa, the first state to caucus in a presidential election.

Rubio said when he agreed to attend the fundraiser, which takes place Saturday, he did so at a time when he “fully believed” Romney would win the election and Rubio would be working for the GOP nominee’s re-election in four years.

In fact, a GOP source told CNN last week that Rubio RSVP’d for the fundraiser in late August at the Republican National Convention in Tampa, Florida.

His comments came in a wide-ranging interview with National Journal’s Major Garrett at the Aspen Institute’s Washington Ideas Forum, where Rubio also spoke frankly about a renewed sense of urgency in his push for immigration reform. He especially charged forward with a call to help undocumented students brought to the country illegally but now face deportation.

“They are more like refugees than illegal immigration folks,” he said, describing the problem as a “humanitarian” issue. “It behooves us to find a permanent solution.”

Rubio, whose parents emigrated from Cuba, has long been an advocate for immigration reform and drafted legislation that supposedly echoed provisions in the DREAM Act, Democratic-backed legislation aimed to help undocumented students gain legal status. The bill failed to garner enough support in Congress, despite several attempts.

Before unveiling his immigration plan, however, Rubio shelved the legislation after President Barack Obama issued a directive earlier this year that allows certain people younger than 30, who came to the United States illegally before age 16, to apply for a two-year deferral from deportation.

Immigration has been a prime topic among Republicans in the days following Romney’s presidential loss. Rubio expanded on the GOP soul searching, saying some in the party could adjust their tone on illegal immigration.

“Unfortunately conservatives have done an excellent job of defining what we’re against but not a good enough job of what we are for,” he said. “What we are for is a legal immigration system that works.”

Asked about Romney’s comment from the Republican primaries that illegal immigrants should “self-deport” and get in the back of the line in their own countries to apply for legal re-entry, Rubio, who was a leading surrogate for the GOP nominee, cautioned against using such language.

“It’s hard to get people to listen to you … if they think you want to deport their grandmother,” he said. “Policy matters, too, but rhetoric is important.”

He later added that illegal immigrants should not be referred to as statistics. “We’re speaking about human beings,” he said.

The senator also weighed in on the thickening battle to find a deficit-reduction deal before an end-of-the-year deadline sets off the so-called fiscal cliff. Included in the fiscal cliff are massive spending cuts that were voted on by Congress and approved by Obama last year as an incentive for lawmakers to find a deal. If they failed to act, the bill stipulated, the country would face $1.2 trillion in automatic, across-the-board spending cuts starting in 2013.

Rubio, who voted against the bill in 2011, said the sequester “was a dumb idea and it’s a dumber idea today.”

“It was bipartisan dumb,” he added. “People want bipartisan. There you have it.”

Rubio, however, stressed he had a strong “economic objection” to the idea of raising tax rates as a way to bring in revenue, the main push being made by Senate Democrats and Obama. He forcefully argued such a policy would severely affect small business owners, while still not raising nearly enough to close the budget gap.

Republicans, meanwhile, propose limiting deductions and closing loopholes in the tax code-an approach Democrats say would also fail to raise enough revenue.

Saying “you can’t cut your way” or “tax your way out of this,” Rubio argued that the economy also needs more robust training and education in order to boost the work force.

Pressed on whether he would vote for a deal that included tax rates, Rubio said he would not “vote for anything that’s not a solution.” Asked to elaborate, he said he would vote for policies that spur “economic growth.”

— CNN Political Editor Paul Steinhauser contributed to this report.