In 2011, the debate over the deficit nearly led to default and brought a downgrade of U.S. securities for the first time before an 11th-hour deal to raise the borrowing limit by $2.1 trillion.
"We all anticipate that the president's request of us to raise the debt ceiling, which will come due sometime this summer, will generate another ... discussion about solving the real problem," Minority Leader Mitch McConnell told reporters. "And we all know the only way to straighten America out is to fix the entitlement issue. Nothing else will get the job done. Only that."
McConnell said he hoped the president "will be willing to step up with us and solve that problem. We're ready to talk about that. And I think the outreach that he's been having is a good thing."
Obama is set to meet with Senate Republicans Thursday after meeting with different congressional groups this week.
McConnell signaled no room for revenue growth, including closing tax loopholes as the president has requested.
"We all know that the revenue side is completely irrelevant to solving this problem," McConnell said.
"And now we need to deal with the spending problem. We're doing part of it -- not a lot, but part of it on the discretionary side, with the implementation of sequester, and the [continuing resolution to keep the government working] will reflect that lower number.
"The second part of the equation is to deal with where the huge expenses are, and that's on the entitlement side," he added. "There is no revenue solution to that, I would say to you. It has to be done by making the eligibility for entitlements fit the demographics of America today and tomorrow.
"Whenever the president's willing to have that discussion, we're ready to have it."