There is one thing that is a mitigating factor here. The Democrats always cave to the Republicans and tuck in their tails if they are afraid they will look bad. They passed the Republican proposal on Health Care reform and caved to the Republicans for not one single vote. They caved on tax increases in 2010. Harry Reid would sell his own child into slavery if he thought it would make him and the Democrats look better--or not bad compared to the Republicans. If the bill is reasonable, they will look very bad for not voting for it, which I think would make it hard for them to vote no at the end of the day.

Besides the Democrats could actually win on this ploy: imagine if they passed this through the Senate, but couldn't get it through the House because of the racist, Tea Party no-vote. This actually seems to me the more likely way it would die, and, if so, it would be the Democrats who would succeed in making the Republicans look terribly bad by actually voting for the measure and proving that the Republicans are actually anti-Latino, as everybody already knows.