Legal Question in Constitutional Law in District of Columbia

No, members of the House and Senate (as well as the Executive Branch: The President) are immune from liability if they act while in their performance of duties. It's called Governmental Immunity.

I agree with Mr. Cook. Additionally, the judicial branch of our government cannot tell the legislative branch what measures to approve or reject. Separation of powers means none of the three branches has that kind of authority over the others.

Even if the courts had this authority, and even if senators and representatives were not immune, I still don't see how you could win such a lawsuit. In order to win you would have to show that the law required the legislators to do what your petition demanded. There is no such requirement. We all have a right to be heard, but even a large majority does not have the right to be obeyed.

The particular amendment you describe would not make much sense. If the Senate and the House could not even vote on their own salaries, how would those salaries be set?

If 98% of Americans wanted an amendment that was actually workable and that didn't conflict with core principles of our nation (your proposal passes this second test, but I can think of others that wouldn't), they would get it through the usual political process without the need for a petition. But if they wanted an amendment that was repugnant to our principles -- say, one that banned a particular religion -- I hope Congress and the states would have the backbone to say no. They certainly would have no legal duty to say yes, just as they would not have to say yes to the petition you propose.