HOUSTON, Texas (KTRK) -- The past week has been one of ups and downs for Texas Gov. Greg Abbott.
His Republican Party maintained its foothold in the Lone Star State on Election Day, with U.S. Sen. John Cornyn and scores of other GOP congressional members holding off Democratic challengers.
In addition, a "blue wave" threatening the political landscape inside the State House of Representatives never came to be.
And if the strides by his party weren't enough, Abbott is holding off on recognizing President-elect Joe Biden as the winner of the presidential race over incumbent President Donald Trump.
Earlier in the week, Abbott insisted "that every legal vote counts and that illegal votes do not," echoing a still unfounded allegation of voter fraud made by President Trump.
In an interview with ABC13's Ted Oberg on Thursday, which you can view in the video above, the governor claimed there were verified instances of votes cast illegally, with some under the names of the deceased.
"What we have seen are verified facts that votes have been cast for dead people," Abbott responded to a question about whether he has seen illegally cast ballots in six states where vote totals were in dispute. "Votes have been cast by people who are not authorized to vote. I haven't seen numbers yet adding it up to being a difference-maker in the presidential race, but they're just beginning to uncover some of the votes that were cast illegally."
Abbott didn't elaborate on those "verified facts" during the interview.
Abbott, though, added that "widespread fraud" could mean anything to anyone.
Beyond the election, Abbott is facing the ongoing threat of COVID-19 in Texas, which became the first state in the U.S. with 1 million cases. Johns Hopkins University said the state surpassed the grim milestone this week.
SEE MORE: Texas now 1st state to surpass 1M COVID-19 cases after setting daily record
Of those cases, 19,337 deaths from the coronavirus outbreak have been counted. And to add to that, the Texas Department of State Health Services has confirmed a case in all but one of the 254 counties in the state.
The governor also offered in the interview above a timeline on when COVID-19 treatments would go out to the Houston area and all other corners of Texas.
Earlier this week, Gov. Abbott announced his plan to distribute COVID-19 vaccines and medicine throughout the state. Among those being distributed this month is antibody drug bamlanivimab, which is manufactured by Eli Lilly & Co.
"Swift distribution of vaccines and medical treatments will begin to heal those suffering from COVID-19, slow the spread of the virus, and aid in reducing hospitalizations of Texans," said Abbott this week. "As we anticipate the arrival of COVID-19 vaccines and treatments, the State of Texas is prepared to quickly distribute those medicines to Texans who voluntarily choose to use them."
SEE MORE: Gov. Abbott's plan to distribute COVID-19 vaccine, medicine