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There's significant incentive for lawmakers to strike a deal. Of those surveyed, 64 percent said shutting the government down for even a few days would be a bad thing for the country. If the standoff were to continue for weeks, 78 percent say they would consider it a bad thing.

"But the difference this time is that President Obama seems much less likely to win the blame game if a shutdown occurs," said CNN Polling Director Keating Holland in a statement. "In 2011, nearly half were ready to blame the GOP if a shutdown occurred, compared to only a third who would have blamed Obama."

Still, President Obama remains more personally popular than Republican leaders. Just a third of Americans approve of House Speaker John BoehnerJohn BoehnerJuan Williams: GOP fumbles on healthcare The Hill's 12:30 Report The new dealmaking in Congress reveals an old truth: majority wins MORE (R-Ohio), and Senate Minority Leader Mitch McConnellMitch McConnellRocky rollout for Senate healthcare bill Overnight Healthcare: Latest on Senate healthcare bill | Four conservatives say they'll oppose | Obama slams bill | Health groups offer scathing criticism Sanders: I hope McConnell listened to protesters outside his office MORE holds just a 24 percent favorability rating. By contrast, 47 percent approve of the president.

Still, the overall sentiment tilts decisively toward dissatisfaction with lawmakers in Washington. Only a quarter of those surveyed said they were happy with the way the country was being governed, while 74 percent said they were dissatisfied.