Aside from the list of things the Constitution actually requires Congress to do being quite short as discussed in other answers, the general answer to this is that there is nothing that can be done. Even forcing Congress to follow its own rules - which each house sets for itself - is not possible.
The Supreme Court considers such cases to be non-justiciable on the grounds that they seek to answer a political question rather than a legal one. The Supreme Court (or the judicial branch as a whole) is not granted any power by the Constitution to force the legislative branch to do anything. They can answer legal questions - such as whether a law passed by the legislative branch violates the U.S. Constitution, what a law means, or how a law should be applied to a given situation, but they can't actually order Congress to take an action.
Each house of Congress sets its own rules, which power is granted by the Constitution itself in Article I, Section 5, paragraph 2. Each house has a rule for how to handle cases where one of its rules is in dispute and those matters - including clarification of the meaning of a rule, determining if something violates it, and determining how to handle such a violation - are settled by that house internally. This is by design in order to ensure that the legislative branch remains independent of the others and able to do its job without outside interference (or not do its job, if it so desires.)
Incidentally, intentionally violating its own rules and abusing the process for rule dispute resolution is how the so-called "Nuclear Option" for (in practice) eliminating the filibuster rule in the Senate worked. Actually changing the rule (according to the rules themselves) requires a two-thirds vote of members present and voting. However, if a ruling on the meaning of a rule is appealed, the Senate itself votes on whether to sustain the appeal - by simple majority. So, they simply appealed the (correct) application of the rule and voted (by simple majority) that the rule does not mean what it obviously did mean. Since such procedures are not reviewable by courts, there was nothing further that could be done about it and the rule was effectively changed in practice, despite lacking the votes to actually change the rule.