In total, 65% of voters said that investigations of election disputes should include forensic ballot audits and 59% of respondents said federal election laws should require paper ballots.
The lawsuit argues that the executive order is unconstitutional.
Harrington said that election integrity was ultimately the most important issue facing the nation.
Rep. Abe Hamadeh said ranked-choice voting is pushed by corporate interests and confuses voters.
The three-question poll asked 1,854 likely voters if they think election workers and officials have enabled fraud, how likely they'll be held accountable, and what the punishment should be.
Kentucky Gov. Andy Beshear signed bill into law this week, similar to a new Wyoming law enacted earlier this month.
Poison-pill legislation? Michigan's National Popular Vote legislation -- pushed by the outgoing Democrats -- "would hand all political power to the large urban areas like New York City and Los Angeles, and it would silence the voices of individual states and the people in those states," Patrice Johnson said.
DOJ previously sent letters to California demanding information about their election practices, and threatened Wisconsin with withholding federal funding for noncompliance with integrity rolls.
A Texas GOP spokesman said the Lone Star State "should be the standard bearer for all things Republican," including election integrity.