Even though Tonkin Gulf Resolution was passed quickly and with an almost 100% vote in Congress (which is super rare), there was still some hearty debate over what the resolution would actually mean. Most of the debate had to do with the President's ability to wage war without needing to constantly ask Congress for permission (that whole "blank check" thing).

Senator Gaylord Nelson ended up voting for the resolution (along with like, 99% of Congress), but he brought up an interesting point in the debate. He said:

[…] am I to understand that […] we are saying to the executive branch […] you may land as many divisions as deemed necessary, and engage in a direct military assault on North Vietnam […]? (Source)

This quote shows us that Nelson (and probably many others) were pretty nervous about handing over so much power to the President. Congress was signing off on giving the President unrestricted access to America's military, and as history shows us, that much strength in the hands of one person can be quite dangerous.

Strongest military in the world, following only a single person's orders? Yeah, we'd be nervous too.

However, it is worth noting that according to the Constitution, the President does have this power as Commander in Chief. Once Congress has signed off on a military engagement, the President has full control of the military. So, Nelson's skepticism was probably more due to the specific situation in Vietnam, and less about what the Constitution actually says.

To put it simply, Nelson probably thought a full-scale invasion of Vietnam was not the best use of America's military might.