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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 BoehnerTrump, GOP fumble chance to govern ObamaCare gets new lease on life Ryan picks party over country by pushing healthcare bill MORE (R-Ohio), and Senate Minority Leader Mitch McConnellMitch McConnellThe Memo: Winners and losers from the battle over health care GOP senators pitch alternatives after House pulls ObamaCare repeal bill Under pressure, Dems hold back Gorsuch support 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.