A New York Times-CBS News poll released Wednesday finds only 16 percent of people believe the threat is acceptable.
The poll comes less than a week before the Oct. 1 deadline Congress and President Obama face. If the sides do not come to an agreement on a continuing funding resolution by then, the government will shut down.
House Republicans — and some in the Senate — have demanded that any funding bill be combined with language defunding ObamaCare. Sen. Ted CruzTed CruzThe Hill's 12:30 Report THE MEMO: Frustrated Trump looks to turn it around Trump: 'No doubt' we'll make a deal on healthcare MORE (R-Texas) spoke throughout the night on the Senate floor arguing against a Democratic plan to strip the ObamaCare language from a House passed bill.
Democrats are set to pass the revised language and send it back to the House over the weekend. Obama has threatened to veto any legislation defunding his signature healthcare law.
According to the poll, Republicans are the most willing to use a government shutdown as a negotiating tactic, but it still amounts to a small minority, 22 percent. Sixteen percent of Democrats and 13 percent of independents believe it is an acceptable negotiating tactic.
More than half, 51 percent, of the public believes Obama is willing to work with Republicans. Only 23 percent believe Republicans are trying to work with the president.
The view that Obama is willing to work across the aisle fell 9 percent since earlier this year, while the Republican number decreased 4 percent.
The poll surveyed 1,014 people and holds a 3-percentage-point margin of error.