Updated: 12:07 p.m.

Senate Minority Leader Mitch McConnell (R-Ky.) invited President Barack Obama to come to the Capitol on Thursday afternoon to meet with Senate Republicans about the debt limit crisis.

McConnell said in a speech on the Senate floor that Obama seemed intent on increasing spending and taxes.

“The president does not seem to get it. So let me do something that I think would be constructive. I’d like to invite the president to come to the Capitol today to meet with Senate Republicans,” McConnell said. “Any time this afternoon he’s available.”

The remarks came just after Senate Majority Leader Harry Reid (D-Nev.) called for the chamber to be in session next week instead of recessing for a planned July Fourth break.

It didn’t sound like McConnell wants the meeting to be a negotiating session.

McConnell said that if the president comes, “he can hear directly from Senate Republicans … why what he’s proposing will not pass.”

National Republican Senatorial Committee Chairman John Cornyn (Texas) challenged Obama to cancel his planned Thursday night fundraiser.

“I wonder if he’s going to cancel his fundraiser in Philadelphia tonight to meet with Sen. McConnell and Speaker Boehner to try and work on this threat that he was so emphatic about yesterday,” Cornyn said. He then predicted that the president would still attend the event.

Cornyn said Obama “diminished the office” of the presidency during his press conference Wednesday. He said the president ought to be ashamed and embarrassed by his own failure to lead on the budget issue.