Hopes of securing a landslide Senate vote in favour of immigration reform were hampered by summer storms on Monday night after several lawmakers were prevented from flying to Washington in time for a key vote.

Nevertheless, the efforts to legalise an estimated 11 million undocumented migrants in the US received a much-needed shot in the arm as 15 Republicans voted in favour of allowing a compromise bill that would toughen border security in exchange for the so-called amnesty.

In total 67 senators voted in favour of proceeding with the revised immigration bill, which includes a border security amendment proposed by moderate Republicans and dubbed a "human fence" or "border surge" because it would double border guard numbers to 40,000.

Twenty seven Republicans voted against the so-called cloture motion, which requires 60 votes to pass and move the bill forward to a final Senate vote this Thursday.

Nevertheless, despite holding open Monday's cloture vote for over an hour to allow for late arrivals delayed by the weather, the Democrat leadership was unable to reach the symbolic 70 votes it had hoped for, with six of the 100 senators absent from the chamber.

Though the target figure of 70 is entirely arbitrary, it points to the biggest challenge facing the bill, which is demonstrating enough Republican support to stand a chance of passage in the much more sceptical House of Representatives.

Democrats and those Republicans behind the bill, such as Marco Rubio and John McCain, hope to convince colleagues in the House that support from immigration reform represents mainstream Republican thinking – particularly after a poor-showing for the party among immigrant groups at the last election.

Anger is growing however among more conservative Republicans at what they see as steam-roller tactics by the party leadership on a matter that is viewed as unpopular among many white voters.

Senator Ted Cruz questioned why there was such a "mad rush to pass a bill" before recess on July 4 when only nine of the dozens of other amendments had even been debated. "Why are we proceeding gangbusters?" he asked. "This amendment is only to tell gullible constituents we have done something. This amendment provides legalisation first and maybe border security maybe later."

Cruz accused the bill's backers of not giving senators time to read its more than 1,000 pages since it was redrafted to include the amendment on Friday.

Democrat sponsor Chuck Schumer insisted only 100 pages contained new material. "Senators ought the able to read 100 pages over the weekend," he said.

The crunch Senate vote will now take place on Thursday before the action moves to the House.

On Tuesday President Obama is holding a meeting with Congressional leaders from both parties during which the immigration reform bill is likely to take centre stage.

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