Appearing on "Fox News Sunday," Cornyn, a leading Republican, criticized Obama for what he said is a failure to put forward a workable solution to the gridlock and impending Aug. 2 deadline to raise the government's debt ceiling.
"What I'm concerned about is the president, by not seriously putting a proposal forward but rather just criticizing those who have, we are running up against this deadline. And they're going to try to present it as a fait accompli, nobody is going to have time to read it or consider the implications of it and it's going to say you have to pass it or the economy is going down the tubes. That's just irresponsible."
Cornyn said the only people that can make a deal to prevent the government from defaulting on Aug. 2 are the president, House Speaker John Boehner, R-Ohio, and Kentucky Sen. Mitch McConnell, the senior Republican in the Senate.
Cornyn said assuming an agreement were reached, it would still be difficult to meet the Aug. 2 deadline.
"It's got to pass the House of Representatives, and then it has to get at least 60 votes in the Senate," Cornyn said. "And we're running out of time."