The Senate also pulled out a change to the Pell Grant program, which provides federal aid to low-income students to attend colleges and universities. Right now, students are considered full time and qualify for the maximum amount of aid if they take 12 credits a semester.

With Sens. Rand Paul and Thom Tillis opposed to the package, GOP leaders can afford only one more defection. And multiple Republicans aren't yet sold on the measure.

Capitol Hill braces for key House vote on Senate-approved legislation as Republican leadership navigates procedural hurdles and applies pressure on reluctant GOP members.