WASHINGTON (AP) — Backers of far-reaching immigration legislation are turning their attention to courting support and counting votes after the Senate pushed the contentious bill over early procedural hurdles.

Two votes to place the bill formally before the Senate and open for amendments each drew more than 80 votes Tuesday, reflecting a bipartisan desire to debate the legislation to remake the nation's immigration laws and open the door to citizenship to millions.

Despite the lopsided votes, Republicans served notice they will seek to toughen the bill's border security provisions and impose tougher terms on those seeking to gain legal status. "This bill has serious flaws," said their party leader, Sen. Mitch McConnell of Kentucky.

At the White House, President Barack Obama insisted the "moment is now" to give the estimated 11 million immigrants living in the United States illegally a chance at citizenship and prodded Congress to send him a bill by fall.

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