Constitutional scholars and even members of the president’s own party say the effort is all but certain to fail. But the looming battle on Jan. 6 is likely to culminate in a messy and deeply divisive spectacle that could thrust Vice President Mike Pence into the excruciating position of having to declare once and for all that Mr. Trump has indeed lost the election…

The dilemma is particularly acute for Mr. Pence, who is eyeing his own presidential run in 2024. As president of the Senate, he has the constitutionally-designated task of opening and tallying envelopes sent from all 50 states and announcing their electoral results.

But given Mr. Trump’s penchant for testing every law and norm in Washington, he could insist that Mr. Pence refuse to play that role. And either way, it will call for a final performance of the delicate dance Mr. Pence has performed for past four years, trying to maintain Mr. Trump’s confidence while adhering to the law.

“The role the V.P. plays in the transition is something that people have never focused on and never think about, but with Donald Trump, you now have to consider all the possibilities,” said Gregory B. Craig, a White House counsel under President Barack Obama.