He said if the law is bad, it will "fall under its own weight."
"Forget about health care. It's going to rise or fall on its own. Forget about energy," he said. "This is about finances. It's about the serious debt we have. It's time to do the reconciliation."
Manchin noted he was not in Congress when the Affordable Care Act was passed. He said he likely would not have supported the legislation, but said lawmakers should stop debating it.
Yet Manchin said Democrats in the Senate and President Barack Obama need to make some concession to Republicans before a budget can be passed.
Rep. David McKinley, a Republican who represents West Virginia's 1st District, said the debate is not over healthcare, but the economy.
He said Republicans knew from the beginning they would not be successful in defunding the Affordable Care Act, but wanted to begin a conversation about the economic effects of the healthcare bill.
Taxes associated with the Affordable Care Act would force businesses to raise prices for consumers and, in some cases, lay off workers, he said.
And while 800,000 federal employees have temporarily been laid off during the shutdown, McKinley said he would not support a "clean" resolution since it would only prolong the debate.
"The clean resolution doesn't solve the problem," he said. "Why can't we just sit down like adults and work our way through this thing?"
McKinley said the House has already appointed a conference committee, but members are waiting for the Senate to do the same.
"Sooner or later, they're going to say, let's just sit down and talk. Once you get that, you've begun going down the right path," he said.
McKinley expects Congress will fight a similar battle over the coming debt ceiling. He said he would only vote to raise the debt ceiling if the bill included provisions for reducing the country's debt.
He pointed to the $1.2 trillion in cuts passed by Congress during budget negotiations two years ago.
"The country has survived. We're forcing things to make decisions. And that's why we're going to see something like that again," he said.
Sequestration cuts have led to decreases in federal Head Start funding for preschoolers, cuts to the Women, Infants, and Children (WIC) program for low-income mothers and billions in military funding.
Rep. Nick Rahall, D-W.Va., was a member of the House the last time the federal government shut down in 1996.
"The stakes are much higher this time," he said. "This is much more serious time for our economy. It's a time when the economy was starting to improve.
"When you start playing with the debt limit, that's a much more dangerous issue for American faith and credit in the world."
Rahall is concerned that Congress will not reach a budget deal before Oct. 17, when the government is expected to hit its debt limit. If that occurs, the government will lose its credit line and be forced to operate only with funds it collects.
Rahall said he was confident a clean resolution would pass the House if it were presented to members, but thinks the government shutdown could last a few more weeks.
Unlike his fellow West Virginians in Congress, Rep. Nick Rahall does not believe everyone is at fault for the shutdown.
"It's a Republican versus Republican issue, and it did not have to happen," Rahall said.
"There are legitimate hardships that are being imposed. These are dedicated public employees who do a great service for the American people. I don't want them to think we're not thinking about them."
Repeated attempts to reach Sen. Jay Rockefeller's office were not successful. A recorded message on the phone line said employees were not available because of shutdown-related furloughs.