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Poll: Just a minority favors defunding health-care law

Despite the health-care law's unpopularity in most surveys, just 38 percent of Americans favor totally eliminating federal funding for it, according to a new CNBC poll released today.

What's more, that 38 percent is cut in half -- to 19 percent -- when respondents are asked if they still supported defunding Obamacare, even if it means shutting down the government and having the government default on its debts.

The CNBC poll -- conducted by Hart Research/Public Opinion Strategies (the same team who does the NBC/WSJ poll) -- was taken of 812 adults (including 201 cell phone-only respondents) from Sept. 16-19, and it has a margin of error of plus-minus 3.4 percentage points.