The administration has everything to do with a new law, and the president doesn't always follow the will of the people. That's why the US is a republic rather than a true democracy. Cap could feel that the administration is leading the people astray by offering this law up as the ultimate answer to superhuman problems when it's obviously not.
Also, the will of the people is not as cut and dried as it would seem. The will of part of the people was to secede in the 1800s, but the government stepped in and said "no." The American Civil War is basically the government telling the people that they're wrong because they're being shortsighted; Cap's doing the same in Marvel's Civil War.