Actually, opposition to the H-1B visa program is a bipartisan thing, just as enacting it was bipartisan as well. H-1B is supported by Al Gore, George W. Bush, John McLame, Bill Clinton.
Many of the folks who oppose the H-1B is just as diverse -- Pat Buchanan, Ralph Nader, Rep. Bob Barr (R-GA), Sen. Tim Hutchinson (R-AR), Sen Tom Harkin (D-IA), fmr Sen. Carol Mosely-Braun (D-IL), Sen. Carl LEvin (D-MI), and Rep. Tom Tancredo (R-CO).