>Explain how immigration is essential to the development and progress of economies, educate people on the implications of immigration.
I'd say that if you want to fix high-skilled immigration, that's exactly the argument you should not make.
What you should do is make an argument that appeals to American culture and sensibilities. Most Americans have ancestors who suffered--some a little, some a great deal--to come to America This is such a strong part of American culture that one of our major holidays, Thanksgiving, basically got it start from the spirit of gratitude that comes from surviving the horrors of trying to immigrate to the New World.
So an argument that boils down to "we're so awesome, how dare you make us bust our balls to become Americans" is going to rub a lot of voting Americans the wrong way. Especially when coupled with a condescending Vivek-Wadhwa-style "you Americans couldn't possible grow your economy on your own, so you should be grateful we immigrants want to come at all." Most Americans expect immigrants to be grateful for the opportunity to come to America, not the other way around.
So, as I said, make an argument that appeals to American culture and sensibilities. In my opinion, the biggest problem with skilled immigration is that 1) H-1B is tied to employment, and 2) so many H-1B visas are consumed fradulantly. So fight against H-1B fraud by insisting on strong enforcement of immigration law. Very few Americans will argue with that, and it will help open up H-1B slots.
And push for H-1B to be decoupled from employment, using the (accurate) argument that the current scheme is basically indentured servitude, a concept that most Americans (as part of our founding mythology) know is a Bad Thing. If H-1B wasn't tied to employment, you wouldn't need a Startup Visa. You wouldn't need the permission of an employer to move to the U.S. And it wouldn't matter (as much) if your green card application took years.