Updated 9:39 a.m. ET, 10/11/2013
Washington (CNN) - Several senior Republican senators from across the ideological spectrum expressed frustration Thursday that the latest proposal from House GOP leaders for a short-term hike in the debt ceiling didn't also include a plan to reopen the government.
"We need to deal with both the continuing resolution and the debt ceiling in a responsible sort of way," said Sen. John Cornyn of Texas, the No. 2 Senate Republican leader. "Obviously just doing part of it doesn't solve the whole problem and we need to solve the whole problem."
"I was surprised that the House decided only to deal with the debt limit and not the continued closure of government," said Maine Sen. Susan Collins, who is involved in bipartisan talks on her own proposal to end the crisis. "I think that we need to deal with both issues and we need to do so quickly."
Collins is circulating a plan that would end the partial government shutdown and increase the debt ceiling. The framework includes a spending measure to fund the government for "probably" six months and a hike in the debt ceiling through the end of January, a source with knowledge of the plan told CNN Chief Political Analyst Gloria Borger. The proposal is still being negotiated among Republican and Democrat senators.
The fiscal standoff was discussed in detail at a closed meeting for all GOP senators in a room just down the hall from the office of House Speaker John Boehner. Earlier, Boehner announced the House would vote to extend the debt ceiling for about six weeks if Democrats agreed to negotiate over a broad range of fiscal issues facing the country.
Sen. Dan Coats of Indiana said the lack of a solution to the government shutdown was his biggest problem with the House plan.
"Nothing is going to work in the end unless both the House and Senate agree to it and the president agrees to it," Coats said.
"I think it would be good to reopen the government," said Sen. Lindsey Graham of South Carolina. But he said raising the debt limit, as the House plan would, is a "start" and "avoids one crisis."
Cornyn suggested Senate Majority Leader Harry Reid could add the government funding to a House-passed debt limit bill and send it back to the House.
But he said it's the "$64,000 question" as to whether the House would accept it.
Meantime, GOP senators said negotiations are underway to find a resolution they hope will be acceptable to House Republicans, Senate Democrats and the White House.
"Negotiations are going back and forth and conversations are going back and forth and I think we need to reach a solution," said Sen. John McCain, R-Arizona, who said there are various alternatives being considered in addition to what Collins is pursuing.
Collins' plan, first unveiled about a week ago, would fund the government, repeal the medical device tax, which is part of Obamacare, and give federal agencies flexibility to deal with the mandated spending cuts known as sequestration. She said other ideas may be added to her proposal.
Democrats have called Collins' plan a non-starter because it would keep the automatic spending cuts known as the sequester in place, something they deeply oppose.
Nevertheless, Sen. Bob Corker, R-Tennessee, optimistically predicted bipartisan negotiations could yield results "very soon."
"There are some very healthy, positive discussions happening on the Senate side," Corker said. "(Senate Republican Leader) Mitch (McConnell) is leading those and many of us are working with counterparts on the other side of the aisle to float some ideas. There have been some very positive discussions in the last 48 hours."
Corker declined to provide specifics of the negotiations, or why he thought a conclusion could be reached soon.