The House has no votes planned this week, as Republicans try to pressure Senate Democrats to fold and open the government.

Hunt also referred to Cornyn's support from GOP leaders in Washington. While Trump has not endorsed anyone in the primary, Senate Minority Leader John Thune, R-S.D., and the chairman of the National Republican Senatorial Committee, Tim Scott, R-S.C., are backing Cornyn.

President Donald Trump's tightening grip over the Justice Department to target his political opponents and lawmakers' increasing calls for the release of more files from federal investigations into deceased sex offender Jeffrey Epstein are likely to take center stage at a contentious Senate hearing Tuesday for Attorney General Pam Bondi.

Democrats need four seats to win control of the Senate but face a daunting political map. A brutal GOP primary is raising hopes in Texas, a state that has dashed Democratic hopes many times before.