House Speaker John Boehner (R-OH) signaled a Republican refusal to budge on the possibility of sending the U.S. into default in a press conference on Tuesday, while accusing President Barack Obama of demanding the GOP give up entirely before even beginning to negotiate.

“What the president said today was, if there’s unconditional surrender by Republicans, he’ll sit down and talk to us,” CBS News quoted Boehner as saying. “That’s not the way our government works.”

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Boehner said he spoke to Obama by phone on Tuesday morning but that he found the president’s position “not sustainable.” He also invoked past negotiations between lawmakers and the administrations of Ronald Reagan, George H.W. Bush and Bill Clinton before mentioning his own discussions with Obama in 2011, but did not mention Obama’s predecessor, George W. Bush.

“While the president suggested today that I walked away from the deal, I would have to remind him that I was in the Oval Office along with [then-]Majority Leader, [Sen.] Eric Cantor (R-VA) when we had an agreement, that two days later, the President walked away from,” Boehner said.

Boehner’s remarks came in response to a public statement earlier in the day by Obama, who reiterated his challenge to GOP lawmakers.

“My suggestion to the speaker has been — and will continue to be — let’s stop the excuses, let’s take a vote in the House,” NBC News quoted Obama as saying. “Let’s end this shutdown right now, let’s put people back to work.”

Boehner quipped that he “didn’t come here to shut down the government,” while casting his stance as a call for fiscal responsibility.

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“This isn’t about me, and frankly, it’s not about Republicans,” Boehner said. “This is about saving the future for our kids and our grandkids. The only way this is gonna happen is [to] in fact, have a conversation. It’s time to have that conversation.”

Watch footage from Boehner’s remarks, as posted by CBS News on Tuesday, below.