House Appropriations Chairman Hal Hogers (R-KY) said it "remains to be seen" if the two will merge as he walked into a closed-door Republican conference meeting on Tuesday. "But yes -- it's only two weeks away."
Appearing Wednesday on CNN, Rep. Michael Grimm (R-NY) called it a "strong possibility."
"There is a strong possibility, if [Senate Democrats] were willing to sit down and listen to us, that we would put a package together and solve the problems at once: stop the government shutdown and deal with the debt ceiling," he said.
Leadership initially gave in to the party's staunch conservatives as they demanded that the continuing resolution be dealt with first. Now, they're in the middle of the first government shutdown since 1996, and a growing number of Republicans worry that position is not sustainable with the debt limit deadline just 15 days away.
"There's a lot of frustration right now on our part," Dent said.
But it's anybody's guess how Republicans might approach them in a broader package, let alone what they might come up with that Democrats could agree to. The White House and Democratic leaders aren't flinching in their refusal to negotiate on the debt limit.
"Timing-wise, the fact is they are close," said a senior Senate Democratic aide. 'But nothing has changed about Democrats' position that we won't be negotiating on it."