A national Republican group that specializes in opposition research targeting prominent Democratic candidates is starting a new initiative on Wednesday to undercut Gov. Andrew M. Cuomo of New York ahead of his 2018 re-election bid — and sully his image should he run for president in 2020.

Mr. Cuomo is the second possible Democratic presidential contender that the Republican group America Rising PAC has singled out for scrutiny. The other is Senator Elizabeth Warren of Massachusetts, who is also up for re-election next year and considered a possible 2020 contender.

Alex Smith, executive director of the America Rising political action committee, said the group is modeling its very, very early 2020 efforts after what she believed was a highly successful push to brand Hillary Clinton as untrustworthy, years ahead of the 2016 race.

“We were one of the first people out there,” Ms. Smith said. “When you put that narrative out there for voters early, and you give it a big runway, it allows it to really sink it.”