Senator Wayne Morse (Democrat of Oregon) was one of only two Senators to oppose the Gulf of Tonkin Resolution. He opposed it partly because he opposed the war in general, but he also opposed it for constitutional reasons.
Basically, Morse believed that the President could not take actions such as the Resolution would have allowed him to do unless the Congress had already declared war. Morse was saying that, unless Congress declared war, the President could not do the things the Resolution would have allowed him to do.
This part of Morse's opposition, then, was based on the idea of separation of powers. He believed that this kind of massive involvement in a war required an actual declaration of war by Congress.