Paranoia in the Wrong Direction
I doubt if leftists are planning to get more votes via immigration amnesty. For one thing, they can get many of same political advantages by the easier tactic of counting aliens in the census. For another thing, the “problem” of illegal immigration is marvelous excuse for a power grab. It's no wonder the Democrats are dragging their feet.
On the other hand, if the Democrats claim to be pro-immigration, they can get the votes of the second generation—especially if Republicans believe it.
The Foreign Minister of Germany once said to me your country does not dare do anything against Germany, because we have in your country five hundred thousand Germans reservists [emigrants] who will rise in arms against your government if you dare to make a move against Germany. Well, I told him that that might be so, but that we had five hundred thousand and one lamp posts in this country, and that that was where the reservists would be hanging the day after they tried to rise.The German threat, of course, went nowhere. That just might be an indication that immigrants to the U.S. are less dangerous than feared.