With the Senate's comprehensive immigration package passed, Sen. Marco Rubio, R-Fla., on Thursday previewed his next moves for upcoming fall clashes over the debt and deficit.

Having spent much of this year as a vocal advocate for immigration reform, an issue that didn't sit well with the GOP's conservative base, Rubio pledged to oppose funding bills, including an increase in the nation's borrowing limits, unless the measures advance conservative demands for greater restraint on government spending.

Rubio said he would not support a continuing resolution that funds government on a temporary basis unless the bill defunds the president’s signature health care reforms.

“Because of that deep philosophical divide, we can’t pass a budget,” Rubio told a breakfast gathering organized by Concerned Veterans of America and the Weekly Standard. “This is going to take place at the same time that the implosion of Obamacare is happening before our very eyes.”

And with the government expected to hit its $16 trillion borrowing limit this fall, Rubio encouraged his Senate colleagues to resist calls to raise the statutory limit further unless Congress passes a budget that includes a plan to reduce the debt over the next decade.

“Debt discourages growth, it discourages job creation,” Rubio said. “We do still have time to get this right.”

The Thursday morning event struck a bipartisan tone with a keynote address from Democrat Ed Rendell, the former governor of Pennsylvania.

“We are one long-term stable debt deal away from ensuring that we will be the dominant economy of the world for the next quarter of a century,” said Rendell, now co-chair of the bipartisan Fix the Debt group. “We need to do something big. We can’t nibble at the edges.”

If government debt continues to rise at its current pace, Rendell argued, mandatory spending and interest payments alone could consume three-quarters of the U.S. budget, squeezing out many other national priorities.

“Republicans have to get out of this idea that it is evil to raise revenue. … We Democrats have to face up to [chained CPI],” Rendell argued. “Everyone’s going to have to give.”