• Senate Minority Leader Mitch McConnell, R-Ky., suggested that the Supreme Court should "discipline" Sens. Richard Blumenthal, D-Conn., and Sheldon Whitehouse, D-R.I.
• Those senators and other lawmakers have called for Justice Samuel Alito to recuse himself from key cases related to former President Donald Trump.
• McConnell argued that Blumenthal and Whitehouse, who are members of the Supreme Court bar, were "potentially engaged in unethical professional conduct before the court."

Senate Minority Leader Mitch McConnell, R-Ky., suggested Wednesday that the Supreme Court should punish at least two Democratic senators over their calls for Justice Samuel Alito to recuse himself from key cases related to former President Donald Trump.

Sens. Richard Blumenthal of Connecticut and Sheldon Whitehouse of Rhode Island are bound by court rules that "provide for discipline against those who engage in conduct unbecoming an officer of the court," McConnell said on the Senate floor.

Numerous Democrats in both chambers of Congress have called out Alito following reports that flags associated with pro-Trump efforts to overturn the 2020 election results were flown at his homes.

But McConnell singled out Blumenthal and Whitehouse because they are members of the Supreme Court bar.

He argued that the two Democrats ran afoul of the American Bar Association's code of judicial conduct by "privately" asking Chief Justice John Roberts "to change the course of pending litigation."

They are therefore "potentially engaged in unethical professional conduct before the court," McConnell said of Blumenthal and Whitehouse, both of whom are members of the Senate Judiciary Committee.

Whitehouse, in a statement to CNBC, said, "When Mitch McConnell, Leonard Leo and the Wall Street Journal editorial page are all criticizing you about the Supreme Court, it's a pretty good sign you're on the right track."

Whitehouse also pushed back on McConnell's description of his communications with Roberts as "private."

"This was a public letter to the Court on an administrative matter pointing out the lack of any meaningful ethics process to enforce our recusal law, and asking the Chief Justice to act in his administrative role as chief," he said. "This was not some secret request for a justice to rule one way or the other on the merits of a case."

The responses from Roberts and Alito confirm that they also viewed the communication as public, Whitehouse added.

A spokesperson for Blumenthal did not immediately respond to CNBC's request for comment.

Whitehouse and Senate Judiciary Chairman Dick Durbin, D-Ill., in a late May letter urged Roberts to make Alito recuse himself from any cases related to the 2020 election and the Jan. 6, 2021, Capitol riot. That includes a pending case before the court on whether Trump is immune from prosecution on federal election interference charges related to the Jan. 6 insurrection, they noted.

Blumenthal separately wrote Roberts last week to ask that he convince Alito and Justice Clarence Thomas to recuse themselves from the same cases over their alleged conflicts. If the conservative justices refuse, the senator said, Roberts should stop assigning them court opinions or circuit justiceships.

Alito rejected the calls to take himself off the cases, arguing that his wife was the one responsible for flying an upside-down U.S. flag outside his Virginia residence and an "Appeal to Heaven" flag outside a vacation home.

Roberts declined to meet with Durbin and Whitehouse.

McConnell in Wednesday's remarks dismissed Democrats' concerns about Alito's flag controversy as "profoundly unserious."

But he said that the senators' efforts go "beyond the standard disgraceful bullying my Democratic colleagues have perfected," because "recusal is a judicial act."

Blumenthal and Whitehouse "may be under the mistaken impression that their persistent attempts to threaten the federal courts are a permissible use of their legislative office," the Republican said. "But they are officers of the court and bound by a different set of rules than a mere senator."

The Supreme Court, he said, "should take any remedial action it feels to be appropriate."

"The legal profession is in distress. Unethical behavior by attorneys serving political causes unfortunately knows no party or faction," he continued. "It is up to the legal profession to police itself."

"And in the end, this means that courts — including the Supreme Court — must police their officers," he said. "We don't need to appeal to heaven to fix this problem. Just to the Supreme Court's power to police the ethical practice of law among the members of its Bar."

When asked by CNBC what sort of discipline the high court should impose on the Democratic senators, a spokesman for McConnell declined to comment.

The Supreme Court in recent years has come under intense pressure over a string of politically inflammatory appointments, rulings and ethics scandals. In November, Roberts announced the court had adopted a code of ethics, though its lack of any enforcement mechanism left critics largely unmoved.

Whitehouse has sponsored legislation that would impose an enforceable code of conduct on the nation's highest court.