Immigration Reform creates stronger growth, which makes the size of the pie a bit bigger. But a bigger pie does not necessarily mean a larger slice for everyone. The distribution of the pie is what matters more. If immigration reform helps the rich get richer and makes the poor even poorer, then should it be a national objective? Is it worth the trade-off to make inequality worse?
The studies on the change of distribution of wealth caused by immigration reform have been mixed at best. Some say that it will make inequality worse. Much worse. While others say that it would be negligible. It really depends on what is included and excluded from the law; as well as whom is included in the analysis.
Odds are - no matter what is in the package (and even if the package works its way into law or not) - immigrants are going to take low and no skill jobs currently held by native-workers because they are willing to accept lower pay and worse working conditions. This scares a lot of low-wage workers into opposing immigration, but opposing immigration is not necessarily the same thing as opposing immigration reform.
One thing is hard to argue though: "It’s better for low-wage workers to compete against immigrants here legally than immigrants here illegally." This is particularly true if workers are at the bound of minimum wage. Native-born workers can not go under it. Legal immigrants can not either. But illegal immigrants can because they are paid underneath the table anyways. Turning illegal immigrants into legal immigrants makes native-born workers more attractive to employers as you have to pay them all the same anyways. Who are going to hire, a native English speaker or someone who barely has a grip on the language?