Hawley and national Republicans pounced on McCaskill's decision. The state attorney general called her a "Washington liberal" and questioned her reasoning, arguing the senator has not shared enough about her own family's finances. The National Republican Senatorial Committee, the Senate GOP's campaign arm, also contended McCaskill's move shows she has moved too far to the left.

A sexual assault allegation against Kavanaugh — which McCaskill said her "decision is not based on" — has thrown his confirmation into doubt. The accusation, which the federal appeals judge denies, dominated conversation in Washington and on cable news this week as Republicans try to confirm him before the midterms. Hawley supports Kavanaugh's confirmation and wants both him and his accuser, California college professor Christine Blasey Ford, to testify.

Despite the GOP's attacks over McCaskill's Supreme Court vote, some in Missouri say it will have limited effect on her push for re-election in November.

"I am skeptical that many votes hinge on Senator McCaskill's stance on Kavanaugh, one way or the other," Peverill Squire, a political science professor at the University of Missouri, wrote to CNBC. "While his nomination has consumed Washington, it does not appear to be a central issue for most Missourians."

The senator's decision on Kavanaugh had nothing to do with her re-election bid, McCaskill's campaign said. In addition, her campaign noted that polling in Missouri generally shows voters care most about health care. McCaskill has slammed Hawley on the issue, as he joined other state attorneys general in signing on to a lawsuit challenging pre-existing conditions coverage under the Affordable Care Act.