They didn't in 2000.
And they didn't (again) in 2004.
Why should I think they will pay attention this time?
They'll pay attention if they get defeated in the primaries, especially if the candidate that's put up by noble citizens holds the same principles on the issue.
Get real here. All they care about is the $$$ flowing in and the votes that go their way. Well people have been whining and moaning about immigration since I've been here, threatening to cut off whatever $$$ they were sending, yet the GOP continues to set fundraising records year after year.
Only an insane person continues to do the same thing and expect a different result. Threatening to cut off funding won't do it.
Voting them out WILL. Push candidates that are similiar to what you believe in. If they lose, they lose. Maybe you can get your guy close enough to the incumbent to either shake him or her up to the issue OR win it outright.
Abandoning the process won't do anything, because that WILL get Democrats elected. I'm SO sure they would do anything about the border.