Sen. John Cornyn (R-Texas) suggested that Republicans are not open to raising taxes as part of a debt-ceiling increase compromise, be it through straightforward tax increases or indirect ones such as closing tax loopholes and ending certain subsidies.

"Let me be just as clear, as clear as I know how. We're not for raising taxes through the front door or the back door during a fragile economic recovery because we think that would make the unemployment worse, not better," Cornyn said on MSNBC. "So that's really, the bottom line as far as I'm concerned."

A bipartisan debt-ceiling increase commission led by Vice President Biden has reportedly reached an impasse largely over whether to include tax increases as part of a deal to raise the debt ceiling. Democrats have demanded that additional revenues be included in the deal, such as tax increases on the wealthy and ending subsidies for the largest oil-and-gas companies. Republicans have voiced strong opposition to including any sort of tax increase as part of a deal.

The Treasury Department says that if lawmakers do not reach a deal and extend the debt ceiling before Aug. 2, the U.S. will default.

On Sunday, Sen. John McCain (R-Ariz.) noted that Sen. Jon Kyl (R-Ariz.), who had participated in the Biden talks, suggested that a middle ground could be found between Republicans and Democrats on additional revenue in a compromise.

"Jon Kyl was in negotiations, as you know with the Vice President, and he said there were certain revenue raisers and other areas that perhaps we could work on, but to somehow say that we weren't going to raise Americans' taxes — anybody's taxes, I think, is a principal we promised the American people last November and that we're going to stick to," McCain said.

There has also been talk of a short-term debt ceiling extension. On Saturday, former President Clinton suggested that President Obama pursue a six- or eight-month extension if Republicans refused to agree to additional revenues in the final deal. On Tuesday, Cornyn suggested that Clinton's extension might be the only viable option. 

But some top House Republicans have voiced opposition to a short-term increase.

House Majority Leader Eric Cantor (R-Va.) “has said repeatedly that he doesn't think a short-term deal could pass the House,” a Cantor aide said Tuesday.

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