Sen. John CornynJohn CornynCornyn: Border wall 'makes absolutely no sense' in some areas Ryan on border: ‘We will get this done’ Ryan tours Mexican border on horseback MORE (R-Texas) took to Fox News on Sunday to attack ObamaCare on Medicare Advantage

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"This is sort of a repetition of 'If you like what you have, you can keep it' false promise, because many seniors are finding that the $300 billion that has been cut out of Medicare has been then used to try to fund ObamaCare," Cornyn said Sunday afternoon, two days before his primary.

"Medicare Advantage has been a tremendous success, it's growing because seniors like the innovation, the choice and the range of services that they have have available to them, but this of course threatens this private-sector alternative and will force people into a single-payer option."

Republicans have been hammering Democrats on a planned 2-percent reduction in payments to Medicare Advantage programs, seeking to further erode support for ObamaCare.

Cornyn has been a vocal opponent of the law from the start, and has ramped up his criticism of ObamaCare leading into his primary against Rep. Steve StockmanSteve StockmanWhy Republicans took aim at an ethics watchdog Cruz will skip State of the Union Ethics: Lawmakers didn’t ‘knowingly’ break rules with Azerbaijan gifts MORE (R-Texas). He is expecting to win the race easily.