Some Republicans fear, though, that the blame could easily shift their way, and initial polls bear out that worry, showing more than six in 10 Americans disapprove of the GOP's handling of the budget negotiations that led to the first government closure in nearly two decades.
An ABC News/Washington Post poll shows 63 percent of Americans don't like the Republicans' approach to the budget impasse, while about 56 percent dislike the Democrats' effort.
Those numbers could shift depending on how long the government closure lasts, and, given the election hits Republicans took after the last shutdown in 1996, longtime GOP members are worried.
Sen. Lindsey Graham, R-S.C., said the repercussions for Republicans will depend on how well the Affordable Care Act, also known as Obamacare which GOP is trying to halt is eventually perceived. The GOP-led House has tied any future government spending to efforts to delay or cut funding for the 3-year-old health-care law.
"We won't get punished for trying to fight the good fight against a bad idea," Graham said. "If it turns out to be a good idea, then we'll be in trouble."
Sen. John McCain, the Republican Party's 2008 presidential candidate, has disagreed with the strategy pushed by Sens. Mike Lee of Utah and Ted Cruz of Texas to use the government's budget as leverage to kill the health-care law. McCain says it's wrongheaded and will cost Republicans.
"By wanting to repeal Obamacare using this method defies what the popular will is," the Arizona senator said, who noted he campaigned all over the country for Mitt Romney, who wanted to repeal Obamacare. "That was not the will of the voters. That's what the voters decided."
Democrats, McCain added, are on "safe ground by saying the will of the people, whether I happen to agree with it or not, [is that] they sent people to the Senate here not to accept the House proposal."
Back on the House and Senate floors, the name-calling was well under way as the Office of Budget and Management was telling agencies to close. Reid at one point even said that Republicans had "lost their minds."
Rep. Jason Chaffetz, R-Utah, said the finger-pointing would continue, and he believes the American public will see that the Republicans have been willing to sit down and talk. The House, he noted, has offered up several different proposals.
"It's politics, so both parties are afraid of optics," Chaffetz said. "The reality is the Democrats' characterization of us has never been true. That hollow ground will give way and I think people will see the truth: We want to fund everything but Obamacare."
Of course, that depends on how long people are out of work. email@example.com