A "mini-deal" to extend the debt ceiling for the short term may be the answer for Republican lawmakers and President Obama to reach an agreement on raising the debt ceiling before the Aug. 2 deadline to avoid a government default on its loans.

President Bill Clinton offered up the suggestion during an interview Saturday night, and in the absence of any other agreement, at least one GOP lawmaker didn't outright dismiss it.

"The problem with a mini-deal is we have a maxi problem. And these -- the big problems -- aren't going to go away if you cut a mini-deal. All it does is delay the moment of truth. So I'd say better now than then," Sen. John Cornyn told "Fox News Sunday."

"But if we can't, we'll take savings we can get now, and we'll re-litigate as we get closer to election," said Cornyn, R-Texas.

Republicans refuse to eliminate tax deductions and subsidies that help businesses and individuals reduce their overall obligation to the government unless there's a drop in existing tax rates.

"I think the American people understand that raising taxes grows the size of the federal government. If there's one thing that I think they told us on November 2010 is that they want government to get smaller, not bigger," Cornyn said. "So, the only way to get government smaller, more rational, is to cut spending, not to raise taxes. So, I think we win that."

Democrats say loopholes for wealthy Americans and corporations are unfair tax breaks, and need to be scrapped so that higher income earners contribute more to the Treasury's coffers.

"Now, it would be nice if we could keep every tax break, but we can't afford them," Obama said during his weekly radio address on Saturday. "Nothing can be off-limits, including spending in the tax code, particularly the loopholes that benefit very few individuals and corporations."

Clinton said since the GOP won't agree on increasing the revenue side of the government's accounting ledger, Obama should consider a "mini-deal" to give the two sides time to sort through the thicket of tax rates and deductions.

"I hope they will make a mini-deal," Clinton reportedly told The Atlantic. "There are some spending cuts they agree on ...and (President Obama) can take those and (get) an extension of the debt ceiling for six or eight months. I don't think you can agree to some mega-deal on their terms."