The Treasury's Aug. 2 deadline is looming, but the chairman of the House budget committee doesn't think the solution to the debt ceiling impasse is happening soon.

"I don't think you're going to see some big bargain hatched today," Rep. Paul Ryan (R-Wis.) said Thursday morning.

The president is holding further budget deficit talks Thursday with Republican and Democratic leaders from both chambers of Congress in an attempt to reach an agreement on the debt ceiling. 

Ryan thinks that the deficit talks will require more debate in order to reach a solution. 

"I think the nation deserves a real, honest debate about its future," Ryan said on "Fox and Friends."

In an effort to hear more perspectives on budget issues, Ryan said the House Budget Committee held a hearing to discuss Pentagon spending Thursday morning. "In the majority, you have to work with the minority and accommodate their concerns and their issues," he said.

On Wednesday during the White House Twitter town hall, Ryan tweeted a question to Obama: "Fearmongering won’t solve our debt crisis. Americans deserve a real debate. You pick: when and where?"

Although Ryan sent the tweet with the #AskObama hashtag used for town-hall questions, Ryan subtly jabbed the president's digital accessibility when asked whether the president responded to his challenge. 

"I don't think he tweets," Ryan said. The president cautiously typed out a tweet Wednesday at the commencement of the Twitter town hall, but White House staff typically run his official Twitter feed.