(CNN) As President Donald Trump prepares for a rollout of a nominee who could solidify the rightward tilt of the Supreme Court for decades to come, judicial conservatives are maneuvering, largely behind the scenes, to ensure that the President gets it right.

The stakes are high, as a Supreme Court seat is a lifetime appointment and conservatives want to make sure the candidate will be a reliable vote.

In a ritual repeated with every Supreme Court vacancy, interest groups and those supporting potential picks are working to boost their favored candidate's chances and jockey for the best position. The President has made clear that he will select a nominee next Monday from a list drawn up with the blessing of the conservative Federalist Society.

It is unclear if the campaign, little of it in the public's eye, will influence the White House, which is keeping its search process largely under wraps.

Many conservatives have been delighted with Trump's first pick, Neil Gorsuch, and are looking for a similar candidate who will be what they consider a reliable vote on the court. Trump called the Gorsuch choice a "homerun" in a Tuesday night speech.

The President has already interviewed several candidates from his list, including Judges Brett Kavanaugh, Raymond Kethledge, Amy Coney Barrett, and Amul Thapar, according to sources. Other sources say that Judges Joan Larsen and Thomas Hardiman are also in play.

Boosters of other candidates are turning their attention to Kavanaugh, a former clerk of Justice Anthony Kennedy's, who sits on the United States Court of Appeals for the DC Circuit and has appeared to be an early front runner. Kavanaugh has a long paper trail of some 300 opinions.

Some social conservatives — while refusing to go on the record — criticized two of those opinions, one dealing with the Affordable Care Act and a second about an undocumented pregnant teen who sought an abortion.

In 2011, Kavanaugh's court ruled in favor of the Affordable Care Act. While Kavanaugh dissented from that ruling, he also said that he would have ruled that the court did not have jurisdiction to hear the case because of a longstanding federal statute that limits the jurisdiction of federal courts to hear tax-related matters.

Critics of Kavanaugh say he should have voted straight out to invalidate the controversial statute.

"On the whole there is a lot in Judge Kavanaugh's record to admire. This opinion, however may be an outlier because he showed too much of a hesitancy to critically interpret the law Congress actually wrote," said Josh Blackman, a law professor at the South Texas College of Law in Houston and the author of Unprecedented: The Constitutional Challenge to Obamacare.

Pointing to that opinion, one judicial conservative who declined to go on the record said "there is a rising doubt about the steadfastness of his views and his commitment to originalism and constitutionalism. "

More recently, the DC Circuit ruled in favor of the undocumented, pregnant teen who sought an abortion. Kavanaugh also dissented from that ruling, but a source who opposes abortion rights who was only willing to speak on background, said concerns have been expressed privately to the White House that Kavanaugh's dissent should have gone farther.

Supporters of Kavanaugh dismiss the attacks and note that he has impeccable credentials, having served in the Bush administration and then as a judge on one of the most important appellate courts in the country. They point to the vast number of opinions he has issued that offer a window into his jurisprudence.

Those include conservative votes in areas concerning presidential authority, the Second Amendment and religious liberty.

David Lat, an influential blogger at Above the Law believes the attacks on Kavanaugh are unfounded, but he said in a recent post that they "reflect the reality" that his service in the George W. Bush Administration and his trail of rulings means there is "more ammunition that can be fired at him."

Still, a senior GOP aide familiar with Supreme Court discussions said on Tuesday that Sen. Rand Paul's office has expressed concerns to the White House on Kavanaugh's Obamacare dissent as well as a 2015 opinion about the government's bulk meta data collection program. The source said that Paul spoke by phone on Monday with the President. GOP and White House sources also say that Sen. Ted Cruz expressed concerns about Kavanaugh to the white house.

A source who opposes abortion rights, who was only willing to speak on background, is pushing for Barrett over Kavanaugh. Judge Barrett drew attention in her own recent confirmation hearings when she was grilled by Democratic Sen. Dianne Feinstein about some of her academic work on religion.

Above the Law's Lat wrote that "the strategy of painting Barrett as some sort of a religious zealot, based on her Catholic faith and her teaching at a Catholic institution backfired" for Feinstein and the Democrats.

Publicly, groups like the National Right To Life, have not come forward to support one candidate over another.

Others have suggested that Barrett might be an ideal candidate for the Supreme Court, but like Larsen and Thapar, they might benefit from more time on the bench.

Kavanaugh actually clerked with Gorsuch back in 1993. Although Gorsuch had been hired by Justice Byron White, White had retired and Gorsuch was assigned to help Kennedy's chambers where Kavanaugh was a clerk.

Neil Gorsuch and Brett Kavanaugh (upper row, left to right)

Multiple sources say Kavanaugh is a long time favorite of White House Counsel Don McGahn It was Kavanaugh who swore in McGahn when he became a commission of the Federal Election Commission in 2008.

The two men also share a disdain for the so called "administrative state" and believe courts should not show too much deference to federal agencies.

Kethledge, another former clerk of Justice Kennedy, has shared similar concerns. He received the support of conservative commentator Hugh Hewitt in the Washington Post this week.

"The search for Gorsuch 2.0 is underway in the White House," Hewitt wrote and called Kethledge "just like Neil Gorsuch" for his adherence to a judicial philosophy championed by Justice Antonin Scalia called originalism.

Other candidates including former Scalia clerk Joan Larsen and Sen. Mitch McConnell favorite, Amul Thapar are still very much in play. And another, Hardiman, who was a Trump favorite for the Scalia seat has gotten less attention this round, but sources say he should not be discounted.