The House took a symbol full-repeal vote last month, but has focused more realistically on trying to cause or exploit problems for the law's implementation and cut off funding for certain elements.
Only 8 percent of likely voters in the Morning Consult poll said Congress should delay or defund the law.
By contrast, 52 percent said Congress should either let the law take effect or make minor changes to improve it. Twenty-three percent said lawmakers should leave the healthcare overhaul alone, while 29 percent supported making minor changes to improve the law.
Overall, public opinion of the healthcare law was mixed. Forty-nine percent said they disapprove of the law, compared with 43 percent who approved.
That's a slightly higher favorability rating than other polls have found, but it's consistent with the overall trend of divided opinion that leans negative.
Most voters also do not expect their lives to improve because of ObamaCare, according to the survey. Asked how the law would affect them and their families, 44 percent said they expect it to make things worse, compared with 23 percent who thought life would get better and 23 percent who expect to see little or no effect.
Nearly half — 49 percent — of respondents expect their costs to go up.