(CNN) Americans remain broadly opposed to overturning the Roe v. Wade decision that legalized abortion nationwide, according to a new CNN poll conducted by SSRS, following the leak of a draft Supreme Court opinion that would strike down the landmark ruling.

Sixty-six percent say Roe v. Wade should not be completely struck down, and 59% would support Congress passing legislation to establish a nationwide right to abortion, including 81% of Democrats, 65% of independents and 30% of Republicans, the survey finds.