Under the bill passed by the Judiciary Committee, unauthorized immigrants could not transition into a probationary legal status until DHS has laid out a strategy for the Southern border. And most of those immigrants would not be allowed to apply for green cards until several security benchmarks — such as implementation of a system for employers to check workers’ immigration status and an electronic exit system at major airports and ports of entry — are met over the next decade.

Rubio’s proposal might satisfy a handful of moderate Republicans who are among the most likely to support the bill but would like to be able to say that they improved it on the Senate floor.

But some of their more conservative colleagues are already looking for stricter triggers.

“The people who are involved in this right now say the triggers to make the rest of the bill happen after supposedly there is border security are very weak and ineffective,” said Sen. Jim Risch (R-Idaho), a longer-shot target of the reform proponents. “If that’s the case, it’s not going to get done.”

The first trigger — the mere completion of a border security plan by DHS — “is an insult to our intelligence,” Risch added.