With a slim Republican majority in the Senate and four months before the 2018 midterm elections, President Donald Trump appears to be sprinting toward his second Supreme Court appointment with few obstacles in his way. But some Democrats are arguing for a halt by dragging special counsel Robert Mueller into the fight.

A handful of Democrats has argued that the special counsel's ongoing investigation should preclude Trump from nominating a successor to replace resigning Justice Anthony Kennedy.

While the argument may sound compelling to Democratic partisans, it doesn't have much basis in law or Supreme Court precedent, constitutional scholars tell CNBC.

Mueller's team is looking into potential coordination between the Trump campaign and Russia during the 2016 election, as well as the possibility that Trump obstructed justice. While Trump is under investigation as part of that probe, he has been told he is not a target, The Washington Post reported in April.

Sen. Cory Booker, D-N.J., identified potential conflicts between the nomination process and the ongoing Russia probe in a judiciary committee hearing last week. “I do not believe this committee should or can in good conscience consider a nominee put forward by this president until that investigation is concluded," he said.

Booker also expressed concern that Trump's documented fondness for demanding the loyalty of his appointees could call the impartiality of his Supreme Court picks into question. That in turn, he said, could potentially apply to the special counsel's probe if any legal challenges to Mueller's conclusions make it all the way to the Supreme Court.

“If we’re not going to thoroughly discuss what it means to have a president with this ongoing investigation happening, who is now going to interview Supreme Court justices, and potentially continue with his tradition of doing litmus tests, loyalty tests, for that person, we could be participating in a process that could undermine that criminal investigation,” Booker said.

Sen. Jack Reed, D-R.I., also highlighted the Mueller investigation in his statement on Kennedy's retirement. Arguing that the next justice should be chosen through a thorough and deliberate process, Reed said that if Republicans "try to rush this nominee through they will also be conveniently ignoring the serious investigation into Russia’s pro-Trump campaign interference in our democracy."

Sen. Jeff Merkley, D-Ore., echoed his colleagues, drawing the same line in the sand in a tweet Friday morning.

Merkley tweet