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An immigration overhaul that would legalize millions of undocumented immigrants while boosting border security passed a major test in the Senate on Monday, as lawmakers voted to advance a compromise measure despite resistance from some Republicans.

The Senate voted 67-27 to advance an amendment that was only submitted late last week. Critics complained that the Senate was voting on the 119-page proposal before having a chance to analyze it.

"This is exactly what happened with ObamaCare," said Sen. Jeff Sessions, R-Ala., one of the most vocal critics of the bill. He warned the chamber was voting on a bill "no one has read."

But the tally late Monday was a positive sign for supporters of the legislation. Fifteen Republicans voted in favor of it.

The vote -- which was technically a vote to shut down debate on the amendment -- needed 60 senators to proceed. That it attracted 67 senators effectively demonstrates the entire bill likely has more than enough votes to pass the chamber. Supporters hope it will also nudge the House to act, though that could be a tough sell.

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    "The bill has been dramatically improved with this vote," Sen. Bob Corker, R-Tenn., a co-sponsor of the amendment, said Monday.

    Senate Majority Leader Harry Reid wants to tee up a vote on final passage before the Fourth of July recess.

    Ahead of the vote, President Obama urged Congress to act.

    "Now is the time to get comprehensive immigration reform done," he said.

    The measure voted on Monday 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 pathway to citizenship for some 11 million immigrants living in the United States illegally, who would be permitted to get permanent resident green cards only once all the border changes had been put in place, about a decade after enactment of the legislation.

    Sessions and other lawmakers, though, warned that the mass legalization could happen even if the border security measures were not fully implemented.

    Despite Monday's Senate vote, the bill still faces uncertain prospects in the 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's dead on arrival in the House," Sen. Rand Paul, R-Ky., said on Sunday.

    But the sponsors behind the border security amendment -- Sens. Corker and John Hoeven, R-N.D. -- staunchly defended their effort ahead of Monday's vote.

    "I've seen reports of a '1,200 page bill' no one has read or had time to read," Corker said in a statement, presumably in response to Sessions. "To be clear, the tough border and interior enforcement provisions that Sen. Hoeven and I offered on Friday make up 119 pages added to the 1,100 pages that have been public since May."

    His office said the proposal would require an "unprecedented surge of security" on the border.

    Some conservative groups were skeptical. The Heritage Foundation on Monday warned that the amendment would allow illegal immigrants to "receive amnesty now," with the possibility of more border security "somewhere down the road."

    The Associated Press contributed to this report.