Supporters of immigration legislation rejected a challenge Wednesday from Senate conservatives demanding evidence that the nation’s borders are secure before millions living in the United States unlawfully can gain legal status.

The vote came as lawmakers on both sides of the issue examined a Congressional Budget Office forecast that the bill would fail to prevent a steady increase in illegal residents in the future, even though it would grant legal status to millions already in the country without the necessary papers.

“Illegality will not be stopped, but it will only be reduced by 25 percent,” said Sen. Jeff Sessions, R-Ala., referring to the prediction by the non-partisan CBO.

Only a day earlier, the CBO had cheered supporters of the bill with an estimate that it would help the economy and reduce deficits in each of the next two decades.

The long-term impact of the assessment of future illegal immigration was unclear, with supporters of the measure maneuvering for the 60 votes necessary for passage as early as next week.

A small group of Republicans, including Sens. John Hoeven of North Dakota and Bob Corker of Tennessee, has been trying to find middle ground on the border security issue in recent days, an effort that accelerated Wednesday.

“This is a key moment in the effort to pass the bill,” said Sen. Lindsey Graham, a member of the bipartisan Gang of Eight that drafted the legislation yet who also wants to toughen its border security provisions.

The vote on a challenge from Sen. Rand Paul, R-Ky., showed the bipartisan Senate coalition behind the bill was holding. The proposal was set aside on a vote of 61-37.

Paul said his proposal would require Congress to vote annually for five years on whether the border is secure.

If lawmakers decide it is not, “then the processing of undocumented workers stops until” it is, he said. The decision would be made based on numerous factors, including progress toward completion of a double-layered fence along the U.S.-Mexico border and toward a goal of 95 percent capture of illegal entrants. A system to track the border comings and goings of foreigners is also required.

Many of the same standards are included in the legislation pending in the Senate, but their implementation is not required for the government to begin granting legal status to millions who are currently in the country illegally.

That difference has emerged as a key fault line in the immigration struggle now unfolding in both houses of Congress.

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The Senate took a series of votes on the legislation as House Republican leaders sought to present a friendlier face to Hispanics — a group that gave President Barack Obama more than 70 percent support in last year’s presidential election.

House Speaker John Boehner, R-Ohio, arranged a meeting with the Democratic-dominated House Hispanic Caucus, while rank-and-file members of his party reviewed areas of agreement with faith-based Latino leaders.

“It’s a conversation Republicans want to have,” said Rep. Cathy McMorris Rodgers, R-Wash.

At the same time, though, anti-immigration protesters moved across the Capitol plaza into range of television cameras, raising signs that said, “Do Not Reward Criminals” and “No Amnesty for Illegal Aliens.”