Counting Electoral Votes: An Overview of Procedures at the Joint Session, Including Objections by Members of Congress
Congressional Research Service
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Objecting to the Counting of One or More Electoral Votes
Section 15 establishes a procedure for making and acting on objections to the counting of one or more of the electoral votes from a state or the District of Columbia. When the certificate or equivalent paper from each state or the District of Columbia is read, the President of the Senate shall call for objections, if any. Any such objection must be presented in writing and must be signed by at least one Senator and one Representative. The objection shall state clearly and concisely, and without argument, the ground thereof. During the joint session of January 6, 2001, the presiding officer intervened on several occasions to halt attempts to make speeches under the guise of offering an objection.When an objection, properly made in writing and endorsed by at least one Senator and one Representative, is received, each house is to meet and consider it separately.
The statute states, No votes or papers from any other State shall be acted upon until the objections previously made to the votes or papers from any State shall have been finally disposed of. However, in 1873, before enactment of the law now in force, the joint session agreed, without objection and for reasons of convenience, to entertain objections with regard to two or more states before the houses met separately on any of them.
More:
https://fas.org/sgp/crs/misc/RL32717.pdf