Perhaps, but remember, people don't make laws, and neither do "lawmakers". Special interests and lobbyists make laws.
You really think GWB think most republicans want amnesty?
I would worry more if anyone cared what the public thought. But unless it's an election year, they don't ... and even then, they just worry about what "the independents" thinks because we all know how the party line "I won't throw my vote away" folks are going to vote.
Propose, advocate, yes...unless someone went and rewrote the Constitution, however, it is still the job of the legislature to put pen to paper.