I have to admit that I don't know the nitty gritty details of this particular "take care" challenge, other than Obama is facilitating alien invasion by action and inaction. If Congress doesn't want the US to be invaded, it can remove the president, and put one in who will do the job. SCOTUS has, more than once, told Congress that the remedy is in their hands. IOW, it may find that the president isn't taking care, but it (SCOTUS) has no power to order a remedy.
If Scotus agrees with the lower courts they’ll just allow their bans on Obama’s actions to continue.