“I think we’re on the verge of getting 70 votes … We’re very, very close to getting 70 votes,” Graham said on “Fox News Sunday.”

The South Carolina senator said the bill, which includes a “border surge” plan. would offer sufficient southern border security, saying “We have secured our border in a way I could not have imagined 4 or 5 years ago.”

The Senate could pass a reform package by the end of the week, but the bill could face a tall hurdle in the Republican-controlled House.