No they don't. Votes can be challenged but both the House and Senate would have to uphold the challenge. With 58 Democratic Senators and around 256 Democratic Congressmen what chance to you think there is that that will happen?
Right Congress does have the power to invalidate or not accept Electoral Votes. Typically in a challenge I would say you are right and it would be a completely political decision but this is a horse of a different color since it would require the ignoring of a direct demand of the Constitution affecting the highest office in the land.
And the sessions of the Houses would be televised I believe.
The Court did not hesitate to order Nixon to turn the tapes over even though it forced the greatest constitutional crisis since the Civil War.
This could be high drama on the order of Shakespeare.