(CNN) - As the Senate veers on the edge of a deal to end the partial government shutdown, Sen. Bob Corker, R-Tennessee, said lawmakers have made progress but criticized his own party for having "wasted two months" trying change the health care law using must-pass spending legislation.
Corker has been one of about a dozen Republican and Democratic senators working to craft a deal that will reopen the government, and raise the amount the government allows itself to borrow just two days before the debt ceiling deadline.
"The fact is we've got to figure out a way to move ahead," he told CNN's Chris Cuomo on Tuesday. "In fairness, on our side of the aisle, we've wasted two months, focused on something that was never going to happen."
“I won't say that I did,” he continued. “But a number of folks did, and what we could have been doing all this time is focused on those mandatory changes that all of us know our country needs. And we've blown that opportunity, I hate to say it.”
While they've made progress, Corker cautioned against celebrating just yet.
"But, look, there's a lot of work that's going to be done over the next two or three days. I don't think it's time to spike the football in the end zone yet," he said.
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Sen. Heidi Heitkamp, D-North Dakota, said the Senate has been more effective than the Republican-controlled House in dealing with the budget and debit issues.
"I think it's going pretty well, and I think it's kind of like - not to criticize anyone, but the adults have taken over," she said on "New Day."
If the Senate passes a deal Tuesday, it then goes back to the House, where it's still questionable whether or not the bill would have a future.
"We want to see what they come out with," Rep. Steve Scalise said on "New Day." "Again, there were two different plans we heard were going to pass over the weekend and neither did. We learned whatever we hear the Senate might be getting ready to do, many times they end up doing something different."
Scalise, a Louisiana Republican, is the chairman of the Republican Study Committee, which was instrumental in getting Obamacare measures chained to a number of spending bills that passed the House.
The Democratic-led Senate, however, said it would refuse to take up any measures that tried to change the president's signature health care law. The stalemate resulted in the partial government shutdown that went into effect October 1.
Scalise told CNN's Kate Bolduan he hopes the president will "finally agree to start negotiating to get long-term solutions so we don't have a crisis-to-crisis moment." He added, however, "we'll get it done before the clock runs out."
CNN later learned House Republicans will offer their own plan on Tuesday to temporarily reopen the government and raise the federal debt ceiling while also making changes to Obamacare.
Sen. Mark Pryor, who also appeared on "New Day," said he expects the Senate to reach a deal Tuesday and hopes it will have a strong bipartisan vote, so that it puts more pressure on the House to pass it.
"One of the goals we really set out within our group, look, we don't want 60 votes. We want to get 70, 75, 80 votes on this if we possibly can. We think that really puts pressure on the House to get this passed," the Democrat from Arkansas said.