Republicans are prepared to pass a six-week increase of the debt limit with the hope that President Obama "will look at this as an opportunity and a good-faith effort on our part" to begin bipartisan negotiations on the 10-day-old budget shutdown, House Speaker John Boehner said today.

"What we want to do is to offer the president today the ability to move a temporary increase in the debt ceiling [and] an agreement to go to conference on the budget - for his willingness to sit down and discuss with us a way forward to reopen the government and to start to deal with America's pressing problems," Boehner, R-Ohio, told reporters today. "Listen, it's time for leadership. It's time for these negotiations and this conversation to begin."

Boehner and his most senior GOP colleagues are scheduled to gather at the White House later this afternoon to meet with the president in the West Wing.

"We have seen now for 10 days a government shutdown," House Majority Leader Eric Cantor, R-Va., said. "It's not what we asked for; it is what was the result of the two parties not being able to sit down and talk. There is very little time left. We cannot waste any more time."

Asked what it would take to reopen the government, Boehner responded coyly, "I don't want to put anything on the table. I don't want to take anything off the table."

"I think the president wants to deal with America's pressing problems just as much as we do," Boehner said. "But in order to deal with these pressing problems, we've got to sit down and have a conversation that leads to a negotiation that begins to solve these problems for the future and for, frankly, our kids and our grandkids."

But most rank-and-file Republicans leaving the meeting maintained they will keep fighting as the shutdown continues to delay the individual mandate in the Affordable Care Act.

"When it comes to Obamacare, we're going to continue to hold our ground," Rep. Raul Labrador, R-Idaho, said. "The American people need to be treated just like businesses were treated which is a one-year exemption from the mandate. It's so the American people don't get taxed for a program that's not even working. You can't even sign up for the program right now and you're going to get taxed if you don't sign up for it."

Rep. Michele Bachmann, the chairwoman of the Tea Party Caucus, said, "What people want is just the option to buy health insurance through Obamacare. They don't want to be forced by Obamacare. It isn't that he would have to give up Obamacare, but just allow Americans the freedom to say, 'Sure, I want it,' or 'No, I don't. I like what I have already.'"

While most of the Republican conference seemed to embrace leadership's latest strategy for a clean debt-limit increase, Rep. Steve King, a fierce critic of the health care law, indicated he would likely oppose the plan when it comes to the floor to a vote this week.

"I'm not very enthusiastic about that [strategy]," King, R-Iowa, told reporters as he hurried out of the meeting.

Boehner, asked explicitly whether he would reopen the government if the president doesn't agree to any changes to "Obamacare," indicated he would not entertain hypothetical questions.

"If ands and buts were candy and nuts, every day would be Christmas," Boehner said, repeating a one-liner he has used throughout his tenure as speaker.