It’s somewhat murky what the birthers expect, should they actually win any of their court cases against the Electoral College. Two losing elector candidates in Minnesota are suing the Secretary of State of California in Grinols v. Electoral College. If Grinols has any standing at all, it must be his injury at not being in the Electoral College because, as he alleges, the winning party’s candidate was ineligible. How the California Secretary of State does anything for a Minnesota elector is unknown.
It’s too late anyway. There is a law, 3 USC § 5, that says any controversy over the electors must be resolved 6 days before the date the Electoral College votes on December 17. The Grinols suit was filed 5 days before.
If any State shall have provided, by laws enacted prior to the day fixed for the appointment of the electors, for its final determination of any controversy or contest concerning the appointment of all or any of the electors of such State, by judicial or other methods or procedures, and such determination shall have been made at least six days before the time fixed for the meeting of the electors, such determination made pursuant to such law so existing on said day, and made at least six days prior to said time of meeting of the electors, shall be conclusive, and shall govern in the counting of the electoral votes as provided in the Constitution, and as hereinafter regulated, so far as the ascertainment of the electors appointed by such State is concerned.
The National Archives explains it this way:
States must make final decisions in any controversies over the appointment of their electors at least six days before the meeting of the Electors on December 17, 2012. This is so their electoral votes will be presumed valid when presented to Congress. The deadline for resolving any controversies is December 11, 2012.