The vote so far clearly indicates that this amnesty and legalization bill is not supported by conservatives, so I don't know where the announcer referenced in the OP got his "facts" that conservatives would support this injustice against American citizens.
Though siding with true centrists in wanting to kill the bill, many conservatives have faced the facts and they know that if the 20 million illegals receive citizenship it will sound the death knell for the Republican Party, the party to which most conservatives belong, as the majority of the 20 million illegals, once pardoned and legalized, would vote for their working-man kin and commonly known champions: the liberal Dems.
Thus many conservatives are against the bill for different reasons than the great majority of Americans, those who are centrists.
True centrists, those who support both liberty and justice for all American citizens, are opposed to anything that deals such a blow of injustice to American citizens as passing this bill would do.
Many conservatives simply don't want the liberals, the Democrats, to thus obtain nearly ever-lasting power that passing this bill would cause even if not passing this bill means comparatively higher wages would be paid to workers at owner-management expense, business owners being the darlings of the Republican Party.