Two high-profile Republican candidates in Texas are under fire from their Democratic opponents for declining to participate in debates, long considered a cornerstone of U.S. democratic traditions.

On Friday, State Rep. Gina Hinojosa, the Democratic gubernatorial candidate, lambasted Gov. Greg Abbott after he missed the deadline to accept an invitation to a debate hosted by NBCUniversal Studios and Texas' Hearst Newspapers.

Sign up "Absent Abbott is scared to debate me because he's a weak governor who's afraid to face his failed record," Hinojosa said in a statement.