Judge Jeremy Kernodle of the Eastern District of Texas said on Friday that Gohmert and the others lacked standing to sue. In a filing late Friday, Gohmert and other plaintiffs filed a notice of appeal to the Fifth Circuit of the US Court of Appeals.
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Gohmert's suit is part of a GOP attempt to overturn the presidential election alleging mass voter fraud and charging that multiple states that President-elect Joe Biden won illegally changed their voting rules due to the pandemic.
Those arguments have failed dozens of times in state and federal courts over the past two months.
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Gohmert and a slate of would-be Trump electors from Arizona had said only Pence could decide what electoral votes count -- an argument suggesting vice presidents can directly determine who wins a presidential election, regardless of the results.
Kernodle, who was nominated by Trump and confirmed in the Senate by voice vote in 2018, wrote that Gohmert "alleges at most an institutional injury to the House of Representatives. Under well-settled Supreme Court authority, that is insufficient to support standing."
As for the group of Arizona Republicans, who claimed that Biden's electors in the state were unlawfully certified, Kernodle wrote that they "allege an injury that is not fairly traceable to the Defendant, the Vice President of the United States, and is unlikely to be redressed by the requested relief."
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Kernodle does not get into the constitutionality of the Electoral Count Act or Pence's ceremonial role overseeing the certification process in his 13-page opinion. Pence on Thursday asked Kernodle to reject the case, arguing that the legal issues from Gohmert should be directed to the House and Senate, rather than the vice president. Pence's filing did not say if he would entertain the possibility of interfering in the Electoral College count, but there is no public indication that he will.
"(A) suit to establish that the Vice President has discretion over the count, filed against the Vice President, is a walking legal contradiction," Pence said. "Ironically, Representative Gohmert's position, if adopted by the Court, would actually deprive him of his opportunity as a Member of the House under the Electoral Count Act to raise objections to the counting of electoral votes, and then to debate and vote on them," Pence's filing added.
A number of Republicans in the Democratic-majority House have already said they will object on Trump's behalf. They only needed a single senator to go along with them to force votes in both chambers. Gohmert said in the lawsuit that he will be one of those objecting from the House. Republican Sen. Josh Hawley of Missouri said Wednesday he will object, which will force lawmakers in both the House and Senate to vote on whether to accept the results of Biden's victory.
Trump, the first president to lose a re-election bid in almost 30 years, has attributed his defeat to widespread voter fraud, despite the consensus of nonpartisan election officials that there wasn't any. Of the roughly 50 lawsuits the president and his allies have filed challenging election results, nearly all have been dismissed or dropped. He's also lost twice at the U.S. Supreme Court.
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It's not clear whether Trump, who remains furious at the Justice Department for its perceived inaction on voter fraud, was informed himself about the ruling. He has taken an interest in Pence's role during the January 6 proceedings, though Pence and others at the White House have tried to explain to him that it's merely a ceremonial post.
House General Counsel Doug Letter filed an amicus brief with the court on Thursday, asking for the Gohmert case to be dismissed, calling it a "radical departure from our constitutional procedures and consistent legislative practices."
"At bottom, this litigation seeks to enlist the federal courts in a belated and meritless assault on longstanding constitutional processes for confirming the results of a national election for President," the House attorney wrote.
The Trump campaign is also continuing its quest at the Supreme Court with the same voter fraud claims. It twice this week asked the court to overturn Biden's win in Wisconsin. Other cases from the President and his allies looking to throw out Biden's victories in Pennsylvania, Georgia, Michigan, Wisconsin and Arizona are pending on the court's docket.
CNN and the Associated Press contributed to this report.