"What's behind it (are) poll numbers that saw Republicans getting their butt kicked because of this whole gamesmanship," Avlon said.
Manchin said the brinksmanship was a chance to address what he called the "draconian cuts" of sequestration.
A new round of the across-the-board spending cuts for the military and other non-entitlement programs takes effect on January 15, he said.
As reported by CNN Chief Congressional Correspondent Dana Bash and CNN Senior White House Correspondent Jim Acosta, the main sticking point for now involves how long an agreement would fund the government to end the shutdown and increase the debt limit to enable required federal borrowing.
Democrats want the debt ceiling increase to extend as long as possible to avoid similar showdowns in coming months.
At the same time, they seek a temporary spending plan to reopen the government while formal budget negotiations work out a longer-term agreement that can negate the impacts of the forced sequestration cuts.
Republicans, however, want a longer spending proposal that would lock in the planned sequestration cuts in coming months, with a shorter debt ceiling extension in order to negotiate further deficit-reduction measures.
Watching developments closely in Washington, Wall Street greeted news of apparent progress in the Senate positively. Stock indexes gained in afternoon trading after sharp early losses to start the week. Bond markets were closed for Columbus Day
Political leaders were mindful of the impact on financial markets if they signaled possible failure to avoid a default.
"I believe we can do it," Democratic Sen. Dick Durbin of Illinois said Sunday on NBC's "Meet the Press." "I hope sensible people prevail, because at this point, it's not just a shutdown and all of the damage it's caused, but if we default on our debt, it will have a dramatic impact on the savings account, on the retirement account of average Americans."
On the other side of the aisle, Republican Sen. Rob Portman of Ohio said he also thinks Congress will find a way out of the crisis before Thursday, when the United States hits the debt ceiling.
"We will have decided as a Congress that we need to avoid going over the debt limit, and we'll figure it out. And it will probably be a relatively short-term solution," Portman said.
A weekend of rejections
Despite the positive prognoses, the only actions over the weekend involved one "no" after another.
• Reid said Saturday the plan Collins was assembling was no longer on the table, because it treated reopening the government as a "concession." Reid continues to demand that any plan include a "clean" bill, one that raises the debt limit and reopens the government with no strings attached. However, Manchin's comments Monday indicated the Collins plan remained alive.
• Republicans blocked a measure to extend the debt limit with no strings attached, refusing to support a procedural vote that would have brought it to the Senate floor.
• House Republican leaders said Obama rejected their proposal for a six-week extension of the federal debt ceiling.
• Meanwhile, Republicans objected to the prospect being floated over the weekend that the forced spending cuts of sequestration, which have cut deeply into federal operations since March, might be rolled back under any eventual deal.
The Treasury Department said it will be unable to pay the government's bills unless the debt limit is increased by Thursday.
Christine Lagarde, head of the International Monetary Fund, said Saturday the consequences of a failure to raise the debt limit would be dire for economies around the world. She spoke to CNN's Richard Quest at an Institute of International Finance conference in Washington.
"You know, I've just spent the last two days with representatives of about 188 countries around the world. I wouldn't say they are confident. I would say they are concerned, and they are very anxious to see this crisis resolved, because they know it's going to impact on their economy," Lagarde said.
Obama spoke by phone with House Minority Leader Nancy Pelosi on Sunday to discuss the ongoing battle over the shutdown, the White House said. The two agreed on the need for a "clean debt limit increase" and a "clean continuing resolution to open up the government and end the shutdown."
Mindful that the Thursday deadline is days away, House Republican leaders are considering all their options even as Republican and Democratic Senate leaders try to craft a deal on the debt ceiling, said a GOP leadership aide, speaking on the condition of anonymity.
One option Republican leaders are considering is sending back a measure to the Senate that would increase the debt limit; exactly what it would contain is unknown at this time.