Without creating a functional (and larger) legal immigration system, they say, the lures for illegal immigration will remain.

But the only hard numbers being thrown around are from immigration reform critics like Sen. Jeff Sessions (R) of Alabama and low-immigrant advocacy groups like Numbers USA, who believe the current Senate bill could double the number of foreigners who gain legal residence over the next decade and add scores of low-skilled workers to an economy with persistently high unemployment.

“Wages have not gone up for the working American over the last 15 or 20 years. My Democrat colleagues have hammered that for a long time, not so much lately,” Senator Sessions said at a hearing earlier this week. “So we have high unemployment, particularly among low-skilled workers, and we have these highly capable people … arguing for more low-skilled workers. And I don’t see how that can be justified at a time we have high unemployment.”

Today, the US allows about 1 million foreigners to become legal, permanent residents every year. The majority of those come by way of family connections, with about one-fifth entering for employment reasons and one-tenth coming to the US as refugees or for asylum.