It can. Check your constitution under duties of the Court. Little known clause. Never as yet used to my knowledge. The concern would be opening a pandoras box, if the other party should ever gain complete control. This is what Gingrich was ineptly referring to when during the republican primary of years past he said, or they (meaning Congress) can just ignore the Court.
The idea that there are three "co-equal" branches is a Myth. The Constitution clearly put the Congress as the superior body to the other two. (Let's not forget the Founders were appointing the Senate; not electing it!) The reality of the executive and Court seizing so much power has always been because of the Congress' insouciance. Congress has the constitutional power to take control whenever they wish but they are now too divided to do anything so dramatic.
This could be the issue however. As even some Republicans realize it is suicide. The red states are going with a plan designed to appeal to the loonies they need to get their governors nominated to run for President, but it will probably make it impossible in a fair election to win in national politics. They are betting everything on being able to control voting. Which, as of now it seems, the Court is poised to let them do, ever since the Court gutted the voting rights act and gave Corporations and political PACs first Amendment rights.
The Court may have already realized that they have placed at risk their perogative to review legislation without oversight by Congress. That perogative was established with Marbury v Madison. Now they have outraged 70% of the American public by ignoring an absurd and ridiculous Texas Law. This matter is not going away until one side or the other gains a clear victory and the matter is put to rest.
I don't think its any exaggeration to say that the character and nature of the nation going forward rides on what happens here.