Gakre
So the power and effect of many of these resolutions is limited to those who can manipulate the majority of the Congress, rather than the President himself in many cases?

The Senate and Congress have been known to hold things up or (as in the case of the past four years being quite evident) not bringing things up at all (House Rep was caught doing that)... yes
And Congress has more power than any.
Process starts with Senate. If passed, goes to "the House" and through Congress. If passed goes to President. If Vetoed by President, Congress may take it up for a vote to either ratify or over-turn the veto (which needs a 2/3 s vote). If P. veto is over-turned, the whole Bill goes back to the beginning to start the whole process all over again.
This is not even taught in schools. There used to be educative commercials "I am a Bill" and all that shown on tv. That is where I learned it from. But you can check that out yourself.
So to answer your question... yes.
Case in point is when Clinton tried to "clean house" when trying to cut spending at The White House. The President has seven - count em - seven personnel that plans and puts into action, the President's traveling activities. Clinton fired four of them. Congress made him hire them all back. That is just one example.