Pelosi told CNN she thinks it has an excellent chance of passing there because GOP lawmakers are the party's poor showing with Hispanic voters in last year's presidential election "sends an eloquent message" to them.
Obama's prodding came several hours before the Senate voted 67-27 to advance the measure over a procedural hurdle. The tally was seven more than the 60 needed, with 15 Republicans joining Democrats in voting yes.
"I think we're building momentum," said Sen. Bob Corker, R-Tenn., who worked with Sen. John Hoeven, R-N.D., on a $38 billion package of security improvements that helped bring Republicans on board by doubling the number of border patrol agents and calling for hundreds of miles of new fencing along the border with Mexico. Those changes brought border security spending in the bill to $46 billion.
"The bill has been improved dramatically tonight by this vote, there's no question," Corker said. "My sense is we're going to pass an immigration bill out of the United States Senate which will be no doubt historic and I think something that's very, very important to this nation."
Last-minute frustration was evident among opponents. In an unusual slap at members of his own party as well as Democrats, Sen. Ted Cruz, R-Texas, said it appeared that lawmakers on both sides of the political aisle "very much want a fig leaf" on border security to justify a vote for immigration.
Senate officials said some changes were still possible to the bill before it leaves the Senate — alterations that would swell the number of votes in favor.
At the same time, Sen. Roger Wicker, R-Miss., who voted to advance the measure during the day, said he may yet end up opposing it unless he wins changes he is seeking.