House Speaker John Boehner says his Republican conference is having trouble coming up with a plan to avoid hitting the government's fast-approaching debt limit, suggesting that even heavenly intervention wouldn't help.

"We are still looking for the pieces to this puzzle," the Ohio lawmaker told reporters Thursday during his weekly news conference. “But we do not want to default on our debt, and we’re not going to default on our debt."

Republicans are opposed to a "clean" debt limit increase without conditions, as Democrats prefer. House Republican leaders reportedly have considered attaching favored GOP measures to a debt limit bill, such as a provision to approve the controversial Keystone XL pipeline and a measure to eliminate so-called risk corridors in the Affordable Care Act. But despite those proposals, Boehner says he still doesn't have the 218 Republican votes needed to pass legislation without Democratic support.

"Mother Teresa is a saint now, but, you know, if the Congress wanted to make her a saint and attach that to the debt ceiling, we probably couldn't get 218 Republican votes," Boehner joked.

Treasury Secretary Jack Lew has warned that the federal government likely will exceed its self-imposed ability to borrow money, or "debt ceiling," by the end of February unless Congress acts. If that happens, the federal government will default on some of its loans, which economists say could trigger a recession, or worse.

"We've got time to do this," Boehner said. "We're going to continue to work at it. No decisions have been made."