According to The Hill, McConnell wants the GOP to vote against Jackson's confirmation to the Supreme Court.
The Kentucky Republican argued that the vote wouldn't be based on Jackson's nomination, despite the fact that she would be the first black woman to sit on the high court.
During a recent Senate GOP lunch, McConnell urged his colleagues to reject Jackson, arguing that the judge on the Court of Appeals for the District of Columbia Circuit had a tough-on-crime approach.
McConnell praised members of the judiciary committee for raising the sentencing issue in the public eye, according to a Republican senator.
He thanked the members of the Judiciary Committee for exposing the judge's radical record and her record on child pornography cases.
McConnell brought up the case of the man who was sentenced to prison in the child pornography case.
When Jackson imposed a prison term of three months, he was 19 years old, and at the time of his arrest, he was 18 years old.
Conservatives have argued that the sentence was too light. The prosecution recommended two years of jail time, while the defense asked for one day in jail and five years of supervised release.
He did not have a criminal record.
McConnell continued to lean into the case during the lunch.
I think the Democrats thought this would be an easy process, confirmation but it is not going to be because she is a radical nominee and I would hope that every Republican would look seriously at her record.
Some potential GOP backers of Jackson in the upper chamber, including Murkowski of Alaska and Romney of Utah, are being put under pressure by the Republican leader's messaging.
According to The Hill, Murkowski was present at the lunch but did not speak to McConnell.
Romney earlier this week said that he was still considering his decision after meeting with Jackson.
The ranking member of the Judiciary Committee, Sen. Chuck Grassley of Iowa, said this week that he was still undecided on Jackson's nomination. He was complimentary of her being very smart in her answers, but also expressed disappointment that she would not state her opinion on expanding the Supreme Court, an issue that she would have no control over if confirmed.
The first Republican lawmaker to commit to supporting Jackson's nomination was Sen. Susan Collins of Maine.
No member of the Senate Democratic caucus has indicated that they would oppose Jackson's nomination. The GOP leader is making his party's messaging more explicit.
Scott Jennings, a Kentucky-based Republican strategist with ties to McConnell, told The Hill that Jackson's nomination fits into the overall message that the Democrats are soft on crime and criminals.
He told the publication that that is going to be a big narrative in the campaign.
Republicans have taken her sentencing decisions out of context and Democrats have firmly rejected that notion. According to the party, Jackson is one of many judges who have sought to have federal advisory guidelines updated since internet-based crimes have become more widespread over the past twenty years.
McConnell described Jackson as very smart but said she wouldn't follow a strict interpretation of the Constitution.
She is a judicial activist. She is very smart and capable. He said she will be a very liberal Supreme Court justice.