So the battle over the Supreme Court could provide Hegar with a much-needed financial boost. Ginsburg's death sent record amounts of cash to Democratic campaigns. It's not clear how much Hegar raked in, but she received more than 200,000 online donations over the weekend, according to her campaign.
Along with Cornyn, three other Judiciary Committee Republicans face competitive reelection races this fall: Iowa's Joni Ernst, North Carolina's Thom Tillis and South Carolina's Lindsey Graham, the committee's chairman. Ernst, Graham and Tillis were facing tight races before Ginsburg's death, however.
Some Republicans weren't concerned about a potential fundraising bump for Hegar.
"The amount of money that would have to flow in would (need to) be utterly staggering," said Chris Homan, a Texas-based Republican consultant. "It's too late in the campaign."
Cornyn's campaign declined to comment on fundraising after Ginsburg's death. Campaign spokeswoman Krista Piferrer said in a statement that the campaign's volunteers who were knocking on doors and talking to voters over the weekend found the Supreme Court vacancy "was top-of-mind."
The vacancy has further highlighted the differences between the two candidates, who took opposing stances on whether the Senate should consider Trump's nominee.
"If the president sends us a nominee, we ought to process the nominee, have a hearing and determine whether they deserve to be confirmed," Cornyn said Monday.
Hegar noted in a Saturday statement that Republicans, including Cornyn, had reversed their positions from 2016, when Senate Majority Leader Mitch McConnell blocked a hearing or vote on President Barack Obama's Supreme Court nominee, Merrick Garland, leaving the seat vacant until after Trump took office.
"We will determine who we are as a country on November 3rd, and it should be the President and Senate we elect who select a qualified individual to serve a lifetime appointment," Hegar said.
As a member of the Judiciary Committee, the battle could take Cornyn off the campaign trail in the final weeks of the race, but the senator didn't seem concerned.