But both the Democratic and Republican Senate leaders have said that adding the immigration provisions to the Iraq funding bill would only bog down the Senate's consideration of the measure, which the White House wants passed quickly.
One Democratic leadership aide, speaking on condition of anonymity, said the House and Senate will probably engage in a "game of chicken" over the fate of the immigration bill -- with the Senate threatening to hold up the Iraq funding measure if it contains the immigration provisions and the House threatening to do the same if they are not included.
That would leave the White House in the awkward position of having to support one side or the other. If it sides with the Senate, it could alienate Sensenbrenner, who could block -- or at least slow -- any guest worker legislation in the House.
In Thursday's vote, 42 Democrats joined with 219 Republicans in passing Sensenbrenner's bill.
All but one of California's 20 Republican House members voted for the bill; the one foe was Rep. Richard W. Pombo (R-Tracy).