They can just take every objection and overrule. It all comes down to this:
IOW no matter how much the Dems object, Repos just need to hold the line and it goes to the governor to decide who are the "real" electors. Done.
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.
IOW no matter how much the Dems object, Repos just need to hold the line and it goes to the governor to decide who are the "real" electors. Done.