Senate Republicans are bracing for an expensive general election in Texas as the state’s scandal-plagued attorney general positions himself to push out four-term incumbent Sen. John Cornyn.

Cornyn faces Ken Paxton in a primary runoff Tuesday, with public polling favoring Paxton. Senate Republicans have fervently backed Cornyn in the primary, saying he would be easier to defend in a general election against the Democratic nominee, state Rep. James Talarico.

Paxton has faced allegations of corruption, financial malfeasance and infidelity. He has also struggled to keep up with Cornyn or Talarico — both prodigious fundraisers — in raising money. Cornyn asserts that Senate Republicans would have to divert essential cash from other competitive races to propel Paxton if he became the nominee.

“It would be hundreds of millions of dollars, and there’s still a good chance he would lose,” Cornyn told supporters Thursday at a campaign stop in Houston.