The check elected officials have on this is to pack the courts. This is what FDR threatened to do to get through (at the time unconstitutional, now magically "not") a bunch of popular legislation.
Only if it could be done in an apolitical way, which seems impossible in the current political climate. The legitimacy of the US Federal Government depends on the perceived continuity of the (now mythical) constitutional order. If one party or the other packs the court without bipartisan support for their nominees in the Senate, it would be denounced by the other as an authoritarian end-run around the constitution--as a revolutionary rather than a mere procedural act. IMO this would be more likely to foment disunion than it would be to restore the bygone constitutional order.
FDR is written about phenomenally in US history books for reasons that don't seem to match the reality of what happened. We can separate foreign policy wins from domestic policy losses, just like we do now.
The now-heralded New Deal was getting torn apart by the Supreme Court, program after program for half the decade. And the remaining parts of the New Deal still exist on shaky constitutional ground if you really look at how much of an abberation they are and how they survived. Spoiler alert, for things that remain its nearly impossible to get standing in Federal Courts to question them and the people that could get standing aren't interested and benefit from them.
FDR threatened to pack the courts, just like modern presidents and party constituents demand.
It was actually very partial that the FDR-era Supreme Court backed off from that threat. So to consider our current Supreme Court to be the aberration is inaccurate, it is even more autonomous.
Everything I look at gives me the opposite conclusion of the public discourse, except when I'm in very small legal circles.
The size of the Supreme court is not defined in the Constitution. So, packing the court is not unconstitutional. It is dishonest and shady as hell. But, the only check on the power of each branch are the other two branches that don't desire to be sidelined by one branch growing more powerful. All three branches are supposed to be in contention for power within the bounds of their interpretation of the Constitution. It is the duty of the other two branches to deem an action of the third branch as unconstitutional.
But, the system has been broken over time. Congress abdicated the majority of their power to the executive and somehow judicial became the official arbiters of constitutionality.