Having Congress assume control of a complex border security overhaul would be a sizable undertaking, but one that speaks directly to complaints from Republican senators that the bill cedes too much authority to the executive branch. Those concerns have been an ongoing theme of tea party activists during President Obama’s administration.

At the same time, Rubio appears sensitive to Democratic objections that unrealistic border triggers would prevent immigrants from achieving legal status, and is trying to develop an acceptable approach.

Already, senators have tailored border security provisions to their liking. Sens. Dianne Feinstein (D-Calif.) and John Cornyn (R-Texas) reached a compromise that would limit drones to within several miles of the border in her state to prevent snooping on such populated areas as San Diego, while allowing a broader surveillance zone preferred by Cornyn in Texas.

Rubio has met with Border Patrol officials in recent weeks to discuss his proposal, and his staff spent the weeklong Memorial Day recess working on revisions, sometimes in consultation with other senators, aides to the senator said.