The Oath of Office for the House of Representatives says:
I do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter: So help me God.
The first part of the constitution says
We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America
So by swearing to uphold the Constitution, they have sworn to "provide for the general welfare". Which they have clearly not done.
So if the House can sue the President for violating the law, can't the Senate sue the House for violating their oath of office?