CHICAGO (CBS) — While chances for sweeping immigration reform have improved with a Senate package of border security measures added to a bill backed by the White House, U.S. Sen. Dick Durbin (D-IL) said the proposal remains chancy in the House.

Durbin estimated the plan would cost “billions” to upgrade security measures along the U.S.-Mexico border.

READ MORE: Chicago Weather: Wind Chill Advisory Overnight, Wind Chills To Drop Well Below Zero

“To give you an idea, in the last 10 years, the Border Patrol has increased in numbers from 10,000 to 20,000. The amendment that will be offered will double it again,” he said.

Durbin said the Congressional Budget Office believes there will be a net positive, given new fees that also are included in the plan.

“For example, anyone who comes into this country on a visa will pay more. The undocumented will be paying, over the span of 13 years, $2,000 a person,” he said.

The measure should also bring in billions more in payroll and income taxes from immigrants who gain legal status.

READ MORE: Chicago Bears Reportedly Expected To Sign Chiefs Exec Ryan Poles As New GM

Durbin said, despite more than $30 billion in costs for border patrol agents and other border security — as well as added costs for Medicaid, Medicare and other federal benefits for immigrants who gain legal status — the CBO estimated the reform package would reduce the deficit by more than $700 billion over 20 years.

While it appears there is enough bipartisan support for the measure in the Senate, its fate in the GOP-controlled house remains unclear.

“I hope that the bipartisan majority in the Senate will convince the Republican Speaker, John Boehner, to reconsider his position. He’s said he’s opposed to comprehensive immigration reform. I think he’s wrong, and I hope that our vote will prove him wrong.”

The Senate is expected to vote next week.

The proposed legislation would vastly increase border fences; double the number of border patrol agents; add more surveillance drones, infrared ground sensors, and airborne radar along the border.

“What I learned during the process of negotiating comprehensive immigration reform was sometimes you just had to bite your tongue, and say the other side of the table is insistent on certain things,” Durbin said. “One of them was a dramatic investment on our border in terms of enforcement.”

MORE NEWS: No States Coming Off Chicago Travel Advisory This Next Week Or Next Week

It also would open the door to citizenship for millions of immigrants who crossed the border illegally. Immigrants now here illegally would face a 10-year path to obtaining permanent residency status, and later eventual citizenship.