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No single entity - not the President, Senate, House of Representatives, state Governors, nor anyone else - has the power to overturn a US Supreme Court ruling.

Raising the question of multiple entities being able to do so.

Supreme Court decisions cannot be nullified by other parts of government.

If no entity can overturn the USSC then the USSC is not co-equal with the other branches but superior to them; a dangerous precipice to place liberty upon.

However, if the Supreme Court strikes down a federal law, Congress can always modify the law until it is such that the Supreme Court does not consider it to violate the Constitution, then pass it again.

What if the USSC is violating a federal law itself? Notably the Conspiracy Against Rights and Deprivation of Rights Under Color of Law felonies, which make no exceptions in applicability to government agents?

Supreme Court decisions can only be overturned in two ways:
1 -- Legitimate Methods

The US Supreme Court reverses a decision on an earlier case by making a contradictory decision on a current case.
Congress and the States can overturn a decision by amending the Constitution.

* That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government... [Declaration of Independence]

2 -- Illegitimate Methods (Passive Resistance)

Sometimes the Executive Branch obstructs or fails to enforce a decision.
Sometimes Congress rewrites legislation to bring it into compliance with constitutional guidelines.
Sometimes Congress strips the Supreme Court of its appellate jurisdiction over certain types of cases to deprive them of the ability to overturn a law or policy.
Sometimes states pass laws that clearly violate Supreme Court decisions, forcing someone with standing to challenge the new law's constitutionality. Meanwhile, the law can be enforced even if violates established civil rights. State legislatures do this with the hope of overturning, or slipping around, precedents set by earlier Courts.

And then there's active resistance...