Can congress be sued by a presidential candidate campaigning during an election year? Can suing congress be part of a candidate's political platform?
As a general matter, governments in the U.S. (federal, state, municipal and tribal) enjoy what is called Sovereign Immunity. It means they can not be sued (except under specific conditions that amount to waivers).
As a legal principle, this is extended from British common law and is called rex non potest peccare which means,
the king can do no wrong.
This is the same principle responsible for the fact that the Queen of England does not need a passport to travel abroad. She is the passport.
That said, however, individual members of congress can be sued for their actions as individuals while in office. But the entire government or branch of thereof can not.
In general, you cannot sue your government due to a common-law practice known as sovereign immunity.
However, some governments have passed laws that allow lawsuits to proceed against them in narrowly defined areas. In the United States, for example, there is the Federal Tort Claims Act, which states:
The United States shall be liable, respecting the provisions of this title relating to tort claims, in the same manner and to the same extent as a private individual under like circumstances, but shall not be liable for interest prior to judgment or for punitive damages.
If, however, in any case wherein death was caused, the law of the place where the act or omission complained of occurred provides, or has been construed to provide, for damages only punitive in nature, the United States shall be liable for actual or compensatory damages, measured by the pecuniary injuries resulting from such death to the persons respectively, for whose benefit the action was brought, in lieu thereof.
With respect to any claim under this chapter, the United States shall be entitled to assert any defense based upon judicial or legislative immunity which otherwise would have been available to the employee of the United States whose act or omission gave rise to the claim, as well as any other defenses to which the United States is entitled.
States, which are also sovereigns, may sue the Federal Government.
3 U.S. Code § 15 (Counting electoral votes in Congress) is almost certainly unconstitutional, and it makes sense for California, New York, Texas, and Florida to seek an injunction to force Congress to correct the constitutional flaw.
My essay entitled "Is the current US presidential election process constitutional? No. Can this process be fixed? Yes." explains the unconstitutionality of 3 U.S. Code § 15.