For context, I will quote from an article that appeared in the Hill early on January 6th:
Under a concurrent resolution approved this week by the House and Senate, two tellers from the Senate and two tellers from the House will take turns announcing the certificates of electoral votes for each state in alphabetical order.
After a certificate of electoral votes for Biden or Trump is announced, any lawmaker may stand up to voice their objection.
The objection must be presented in writing and must have the signature of at least one member of the House and one member of the Senate. It must state “clearly and concisely” the grounds for objection.
At that point, Vice President Pence, sitting in the chair as the president of the Senate, will recognize the objection as complying with the Electoral Count Act, Title 3, Section 15 of the U.S. Code, and order the House clerk to read the objection.
Pence will then instruct the Senate and House to withdraw from the joint session to deliberate and vote separately on the pending objection and report their respective decisions back to the joint session at a later time.
The vice president is required by law to consider the presentation of election certificates of all 50 states and the District of Columbia in alphabetical order. Objections to each state’s electoral votes must be debated and voted on one at a time.
Now, imagine, it's the 2024 election. Trump succeeded in getting a couple of crucial states with Republican trifectas to overturn the popular vote and deliver him an electoral majority. Inevitably, Democrats seek to challenge those "unique" electoral votes in the joint session in January 2025. Say there is a Republican house majority which rejects the challenge. BUT, in the senate, the Democratic minority is joined by enough establishment Republicans (Romney, Sasse, Murkowski say) to give the objectors a slim majority.
So, the joint session reconvenes and discovers that the House voted down the Democratic objection but the Senate voted to sustain it. What happens next?
EDIT: Here is the relevant law
EDIT 2: I figured it out, if the houses disagree it defaults to those electoral votes certified by the state. So both houses would have to reject the electoral votes for them to be discredited.
"But if the two Houses shall disagree in respect of the counting of such votes, then, and in that case, the votes of the electors whose appointment shall have been certified by the executive of the State, under the seal thereof, shall be counted."
I don't think this is going to happen, as by 2024, all three of Romney, Sasse and Murkowski will either have been replaced by Republicans willing to overturn the election (Murkowski), or Republicans will have a big enough majority in the Senate to successfully overturn a Biden victory even without the votes of Romney, Murkowski and Sasse (possible if they pick up Arizona, Nevada and Georgia while losing no seats in 2022.)
