White House Deputy Press Secretary Brian Morgenstern said President Trump's continued election result challenges were part of his commitment to the Constitution and the concept of fair elections on Tuesday.

"The president's policy all along is that he wants free and fair elections," he told "Outnumbered Overtime." "Every legal vote should be counted. That has really been his position. That's why he's had election security as a priority. That's why he has prioritized constitutionalist judges to make sure that the bedrock of our democracy, the rule of law of the United States Constitution, really rules the day."

The Trump campaign has lost nearly every legal challenge in its efforts to overturn President-elect Joe Biden's victory, which Trump insists was "rigged" and the result of massive voter fraud. The Department of Justice led by Attorney General William Barr said it has found no evidence of sufficient fraud to change the result.

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Two Pennsylvania Republicans have brought another lawsuit alleging a 2019 law allowing no-excuse mail-in voting is unconstitutional. If the court agrees, according to KDKA, they claim most of the mail-in votes from the presidential election could be thrown out. Biden narrowly won Pennsylvania after Trump carried it in 2016.

Sen. Ted Cruz, R-Texas, has volunteered to argue their case if it goes before the Supreme Court, although that appears unlikely.

On Tuesday, Texas sued Pennsylvania, Georgia, Wisconsin, and Michigan to challenge their 2020 results, arguing with COVID-19 as a justification, they weakened "ballot integrity" through unconstitutional revision of electoral statutes. Texas is petitinoing the Supreme Court to block their Electoral College results, but experts say that is highly unlikely to occur.

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Morgernstern also discussed the success of Operation Warp Speed, the public-private vaccine effort spearheaded by the Trump administration. The White House held a summit on the vaccines Tuesday as the Food and Drug Administration prepares to hear arguments for Emergency Use Authorization of Pfizer and Moderna's respective immunizations.

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"The thing the American people should take away from this is that we are still on track to have vaccines for all Americans in the first part of 2021," he said.

Fox News' Jack Durschlag contributed to this report.