The Senate headed Monday for the first test vote on the measure offering the prize of U.S. citizenship to millions and pouring new technology and manpower into the border.

Ahead of the vote set for early evening, around a dozen Republican lawmakers had indicated support, setting up a solid bipartisan margin of victory within reach of the 70 votes supporters are hoping for when the bill comes to a final vote at the end of this week. No defections have been suggested so far among the 54 votes controlled by Democrats.

The measure includes changes to the original border security provisions in the bill that would double the size of the U.S. Border Patrol at a cost of around $30 billion and complete 700 miles of fencing. At the same time it sets out a 13-year pathway to citizenship for some 11 million immigrants living in the United States illegally.

“It certainly should put to rest any issue regarding border security,” Sen. Bob Corker, a Tennessee Republican who worked with Sen. John Hoeven, R-N.D., on the border security compromise, said Sunday on CBS’ “Face the Nation”

“And what it does to those who want to come out of the shadows, know that they have a path forward to be a productive part of our country, it answers that, also,” Corker said.

Sen. Chuck Schumer, D-N.Y., a lead author of the bill, was predicting victory.

“Our momentum is growing. So I believe we’ll be in the neighborhood of 70 votes by the time the vote occurs at the end of the week,” Schumer said Sunday on CNN’s “State of the Union.”

These developments came at the start of a crucial week for the immigration bill, a signature issue for the Obama administration, Hill Democrats, and even some Republicans.

Monday’s vote is the key procedural hurdle that would clear the way for a vote later in the week on revisions to the bill including the border security changes and a range of other new provisions aimed at locking down support from wavering senators. These include limits to what newly legalized immigrants can claim in Social Security benefits, added at the behest of Sen. Orrin Hatch, R-Utah, and provisions designed to aid Alaska seafood processers and attract support from Alaska’s two senators.

At the White House, President Barack Obama was to meet at mid-afternoon Monday with business leaders supporting the legislation. And U.S. Chamber of Commerce announced it was launching a new seven-figure ad buy Monday in support of the bill.

Victory in the Senate would be no guarantee of success in the Republican-controlled House, where many conservatives oppose citizenship for people in this country illegally. The House Judiciary Committee has been passing narrowly focused, single-issue immigration bills — in contrast to the Senate’s comprehensive approach — and Speaker House Boehner, R-Ohio, has not indicated how he’ll proceed.

Negotiations between the two chambers are not expected until the fall at earliest, and opponents of the legislation are predicting it will be stopped in the House.

“It will pass the Senate, but it’s dead on arrival in the House,” Sen. Rand Paul, R-Ky., said on CNN on Sunday. “The House is much closer to me, and I think they think border security has to come first before you get immigration reform.”

(AP)