So far, the Democrats seem to be winning that public relations battle, with polls showing a large majority of Americans squarely holding Republicans responsible for the 800,000 federal employees forced off their jobs and the closure of a series of non-essential government services.
Republican attempts to saddle the spending bill with provisions to delay parts of Obamacare is the wrong tactic to take, say many, including those who don't support the law.
Some Republicans are even blaming their own party members for the stalemate they fear will ultimately hurt the party.
"This is Ted Cruz’s fault. Ted Cruz led us down this path," New York Congressman Peter King told Fox News, referring to the Tea Party favourite senator, who led a 21-hour marathon speech against Obamacare. "This was a disaster from the start, I could have predicted this."
- U.S. government shutdown: What's next?
- Neil Macdonald: The perverse math behind the Republican budget showdown
- U.S. government shutdown could make Washington a smelly city
- U.S. government shutdown: What's open and what's closed
Meanwhile, Democrats and liberal commentators continue to use fiery rhetoric to hammer on the same theme — that Obamacare is the 'law of the land,' it's been upheld by the Supreme Court, that Republicans only control one branch of government, and that the Republicans have effectively taken hostage of the government.
"The Affordable Care Act has been the law of the land for four years. Democrats are willing to work with reasonable Republicans to improve this law. But we will not bow to Tea Party anarchists who deny the mere fact that Obamacare is the law," said Senate Majority Leader Harry Reid.
'Bomb strapped to their chest'
Or, as senior White House adviser Dan Pfeiffer said, "What we're not for is negotiating with people with a bomb strapped to their chest."
Writing for the New York Times, columnist Tom Friedman took it a step further and suggested that the fate of democracy is at stake, that Obama should not give in to "this hostage taking" and that the issue is not just about defending health care.
"He’s defending the health of our democracy. Every American who cherishes that should stand with him," he wrote.
Daily Show host Jon Stewart may have summed up much of the sentiment with his expletive-filled rant against Republicans. He also stressed that Obamacare is the law, dismissed the Republican strategy as "utter insanity," and compared the party to a football team losing by 24 points and saying if they don't get 25 points on Monday, they will shut down the NFL.
But Republicans and conservatives are fighting back, pointing their own fingers. It's the Democrats and the president, not Republicans, who are holding the country 'hostage' by refusing to budge, they claim.
While the Republicans may not control all the branches of government, the same could be said about the Democrats, and so they too must be willing to negotiate, some say. Others have sneered that Obama is willing to negotiate with the Iranian president but not House Speaker John Boehner.
“I just think it’s outrageous that Harry Reid will not sit down and negotiate about something that’s troubling to a lot of Americans, and that’s the implementation of the new health-care law,” Republican Patrick Tiberi told reporters.
'They are the dogmatists'
Peter Wehner, former deputy assistant to George W. Bush when he was president, echoed Tiberi's comments, saying that Obama and the Democratic Congress are the "inflexible and unyielding ones."
"They are the dogmatists in this drama," Wehner wrote in Commentary Magazine.
While Wehner said the Republican strategy is politically unwise, he defended it as legitimate and reasonable, saying members of Congress are just using levers available to them.
On Wednesday, Obama summoned congressional leaders to the White House. But even that move was met with some derision. Shortly after the announcement, a spokesman for Boehner shot back: "We're pleased the president finally recognizes that his refusal to negotiate is indefensible."
Many Republicans have also rejected the "law of the land" argument regarding Obamacare. Jay Cost, writing for The Weekly Standard, said the Democrats are basically arguing that once a bill becomes law, "it is as indelible as the Ten Commandments, etched into rock by the hand of God himself."
He pointed out that it was the Democrats who mounted a 10-year campaign against the Bush tax cuts, despite defeat after defeat on the issue. He then listed a number of so-called laws of the land that have been substantially revised or repealed entirely, including: portions of tax cuts initiated by former presidents Ronald Reagan and John F. Kennedy, the gold standard, Prohibition and the Articles of Confederation.
Some Republicans have also accused Obama of hypocrisy. While Obamacare may be the law of the land, the president himself has been willing to delay parts of it, including the mandate that forces businesses to provide health insurance. (Some have gone so far to say Obama's moves are unconstitutional, that only Congress has that authority).
But many analysts, including Republicans, say regardless of who is to blame, the issue is a political loser for the Republicans.
"It's an iron law that Republicans get blamed for any government shutdown, no matter who controls the White House or Congress," former Bush strategist Karl Rove said.