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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 BoehnerRyan reminds lawmakers to be on time for votes Juan Williams: GOP fumbles on healthcare The Hill's 12:30 Report MORE (R-Ohio), and Senate Minority Leader Mitch McConnellMitch McConnellFifth GOP senator announces opposition to ObamaCare repeal bill The Hill's 12:30 Report Spicer: When Trump wants to get something done, 'it's going to get done' 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.