Rep. Beto O'Rourke Beto O'RourkeJimmy Carter says his son smoked pot with Willie Nelson on White House roof O'Rourke endorses Kennedy for Senate: 'A champion for the values we're most proud of' 2020 Democrats do convention Zoom call MORE (D-Texas) is committed to serving out a full term in the Senate if he beats incumbent Sen. Ted Cruz Rafael (Ted) Edward CruzThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Cruz blocks amended resolution honoring Ginsburg over language about her dying wish Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Texas) in November.

In an interview with The Texas Tribune earlier this month, O'Rourke was clear that he planned to serve "every single day of my full six-year term for the people of Texas."

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But the Tribune reported Cruz demurred when asked the same question in a separate interview the newspaper conducted with the senator.

"I am focused on the United States Senate," the Tribune quoted Cruz as saying when asked in an interview earlier this month whether he might run for president in 2020.

The Tribune said it then followed up with another question, "Can you commit to serving out your term?"

The Tribune reported that Cruz started his reply with: "You know, as we stand here today, the Texas Board of Education is getting ready to vote on a proposal, a recommendation they received, to delete the word 'heroic' from the description of the defenders of the Alamo."

That response ended two minutes later with Cruz asserting that "we should be standing up for who we are as Texans and Americans," according to the Tribune.

Speculation has swirled that Cruz and O'Rourke could make runs for the White House in 2020. That speculation has been fueled by the fact O'Rourke's Senate bid has gained significant national attention.

Cruz already ran a competitive presidential primary campaign against Trump in 2016 and he has not ruled out another bid for the White House. Asked by the Tribune this month whether he was planning a 2020 run, Cruz said: "I am focused on the United States Senate."

But Trump is also expected to seek a second term in 2020, meaning that Cruz would likely have to challenge a president from his own party if he mounted a White House campaign.