Before that can happen, both Houses would have to reject electoral votes fraudulently submitted. (3 USC 15)
I don’t see that happening.
Not that it matters at this point, but we have Chambers (House of Representatives and the Senate). It’s the limeys who have two Houses (House of Commons and House of Lords).
But, like I said, it may all be moot now. Even though I know there are other cases in process, it did seem, with something like 20 states signing on to amicus briefs in support of Texas, to be the strongest case.