"We intend to vote on January 6 to reject the electors from disputed states as not 'regularly given' and 'lawfully certified' (the statutory requisite), unless and until that emergency 10-day audit is completed," the group said Saturday in a statement.
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In addition to Cruz, the group includes Sen. Ron Johnson of Wisconsin, Sen. James Lankford of Oklahoma, Sen. Steve Daines of Montana, Sen. John Kennedy of Louisiana, Sen. Marsha Blackburn of Tennessee and Sen. Mike Braun of Indiana. Four senators-elect are also planning to object, including Cynthia Lummis of Wyoming, Roger Marshall of Kansas, Bill Hagerty of Tennessee and Tommy Tuberville of Alabama. The four are scheduled to be sworn in on Jan. 3 when the 117th Congress convenes. All 11 are Republicans.
Sen. Cruz's office told ABC13 he will lead the effort to object to the election results when Congress convenes on Jan. 6.
A joint session of Congress is scheduled to be convened on that date to receive the results of the Electoral College. Any challenge to those results requires at least one member of the U.S. House and Senate.
Under federal law, Congress must meet to open sealed certificates from each state that contain a record of their electoral votes. The votes are brought into the chamber in mahogany boxes. Bipartisan representatives of both chambers read the results out loud and do an official count.
After certificate results from a state are read, any member can stand up and object to that state's vote on any grounds. But the presiding officer, Vice President Mike Pence, will not hear the objection unless it is in writing and signed by both a member of the House and a member of the Senate.
If there is such a joint request, then the joint session suspends and the House and Senate go into separate sessions to consider it. For the objection to be sustained, both chambers must agree to it by a simple majority vote. If they do not both agree, the original electoral votes are counted.
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The last time such an objection was considered was 2005, when Rep. Stephanie Tubbs Jones of Ohio and Sen. Barbara Boxer of California, both Democrats, objected to Ohio's electoral votes by claiming there were voting irregularities. Both chambers debated the objection and rejected it. It was only the second time such a vote had occurred.
Biden's electoral win over Trump was 306-232, though challenges are pending in courts and some results continue to be disputed.
Cruz's challenge comes despite a plea last month from Senate Majority Leader Mitch McConnell that Republican senators not join in the challenge effort. McConnell told his caucus on a private call that it would be a "terrible vote" for Senate Republicans to have to take.
The senators, led by Cruz, called on the appointment of an Electoral Commission to conduct a 10-day audit of the election results in "disputed states." The statement does not list which states should be included, nor does it mention any specific cases of fraud.
"We are not naive," the group said in a statement. "We fully expect most if not all Democrats, and perhaps more than a few Republicans, to vote otherwise. But support of election integrity should not be a partisan issue."
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Texas previously sued to challenge the election results in Georgia, Pennsylvania, Michigan and Wisconsin on the basis that those states implemented pandemic-related changes to election procedures that, Texas claimed, were illegal and cast into question the election results. The U.S. Supreme Court in December tossed the lawsuit.
A federal judge on Friday dismissed a lawsuit by U.S. Rep. Louie Gohmert, R-Tyler, that also sought to overturn the election results.
SEE ALSO: Federal judge dismisses Texas congressman's lawsuit to stop Biden presidency
The Associated Press and the Texas Tribune contributed to this report.