A solid majority of Americans oppose defunding the new health care law if it means shutting down the government and defaulting on debt. The CNBC All-America Economic Survey of 800 people across the country conducted by Hart-McInturff, finds that, in general, Americans oppose defunding Obamacare by a plurality of 44 percent to 38 percent.

Opposition to defunding increases sharply when the issue of shutting down the government and defaulting is included. In that case, Americans oppose defunding 59 percent to 19 percent, with 18 percent of respondents unsure. The final 4 percent is a group of people who want to defund Obamacare, but become unsure when asked if they still hold that view if it means shutting down the government. The Republican-party-led House voted 230-189 on Friday to adopt a short-term government spending bill that would eliminate all funding for the new health care law. The measure could lead to a government shutdown in less than two weeks. The poll, which has a margin of error of plus or minus 3.4 percent, was conducted Monday through Thursday of last week. Full results will be released this Thursday. (Read more: Anxieties mount over Obamacare)

In general, men are roughly split on the issue, with 43 percent supporting defunding, 42 percent opposing and 15 percent unsure. But when the issue of a government shutdown and default is included their support declines: 56 percent oppose defunding and only 14 percent solidly favor the measure. Women are more firmly opposed to defunding the new health care law under any circumstances, with 47 percent opposed, 33 percent in favor and 20 percent unsure. (Read more: You're going to be paying more for this next year)

A 51 percent majority of Republicans generally support defunding with 36 percent opposed and 13 percent unsure. However, when including the issue of a government shutdown and default, the picture changes: 48 percent of Republicans oppose defunding Obamacare, while 36 percent support it. However, a 54 percent majority of Republicans who also identify themselves as Tea Party supporters want the new health care law defunded even if it means a government shutdown – the only demographic measured in the poll with such a majority.

Republicans who do not identify themselves as Tea Party supporters hold views closer to those of Democrats than to Republicans that do identify themselves as Tea Party supporters: They oppose defunding Obamacare 44 percent to 36 percent with 20 percent unsure. (Read more: Obamacare's biggest test: How many enroll?)