Under the emerging deal, an estimated 11 million immigrants living in the United States illegally would be eligible to obtain legal status while border security was increased. They could not be awarded green cards, which bestow permanent residency status, until the entire border enhancement plan had been put into place.
That effectively would give the government a decade to set up the additional security, since the legislation envisions a pathway to citizenship that gives immigrants provisional status after six months but requires them to wait at least a decade before they become eligible for green cards.
Despite the changes, the legislation appeared certain to retain the basic contours negotiated over many months by a so-called Gang of Eight, four senators from each party.
Whatever its impact on the bill's prospects, the deal failed to satisfy a group of conservative Senate critics who want proof that the border has been secured before legalization begins, rather than the mere placement of new agents and equipment.
"My impression is this is a promise of future performance and there is no contingency in the form of a trigger" to assure its effectiveness, said John Cornyn, R-Texas.
Sen. Jeff Sessions, R-Ala., also cautioned that the highly touted agreement had not been drafted yet, much less read by members of the Senate and their staffs.
The legislation has a broad array of outside interests pushing for its passage, although two organizations objected to the plan for changes.
Speaking for CAMBIO, an organization that favors immigrant rights, Christian Ramirez said the deal should include lapel cameras to deter abuse by border agents, as well as the placement of 1,000 distress beacons in the desert.
The ACLU called the proposed agreement a "massive deployment of force" that would be "simply devastating for border communities."