"Most of what I'm doing is by Zoom anyway," he said.
Some Republicans said Cornyn's seat on the committee could help him.
"It's obviously an opportunity for him in terms of being more of a national figure and being visible," Texas GOP strategist Matt Mackowiak said. "That's always helpful because earned media is valuable."
Strategists in both parties believe the high court fight will inject even more energy into the race. Some Democrats also believe it will push critical swing voters in the suburbs, where the party made gains in 2018 House races, further into their corner.
"I see all of this really revving up the Democratic base but also appealing to suburban women who may have been conservative in the past but are not seeing any kind of reason to stay with the Republican Party," Texas Democratic consultant Sonia Van Meter said.
Not a game-changer? While the Supreme Court battle could boost fundraising, energy and attention around the Senate race in Texas, it may not fundamentally alter the contest.
Democrats remain laser-focused on health care, quickly tying the Supreme Court vacancy to the Trump administration's lawsuit to dismantle the 2010 health care law. The high court will hear arguments in the case one week after Election Day.
"I kind of doubt it's a dynamic-changer," said Jim Henson, director of the Texas Politics Project at the University of Texas at Austin. Henson noted that independent voters who don't have strong ideological leanings do not view the Supreme Court as a top issue.
And for Hegar, those independent voters are critical.
"A third of Texas self-identifies as independent," Hegar said Tuesday at a Texas Tribune Festival event with The Washington Post. "I believe we are an independent state that has been a low-voter state for a long time."