Vowing that they have learned the lessons from the 1986 amnesty, the Senate on Thursday approved the biggest changes to the immigration system in a generation, promising this version will prevent another wave of illegal immigrants while granting a pathway to citizenship to most of the estimated 11 million illegal immigrants already in the country.

The 68-32 vote, in which 14 Republicans joined all 54 of the chamber’s Democratic caucus members in support, is likely the high-water mark for immigrant rights advocates, who held prayer vigils and packed the public viewing galleries during the vote, anticipating good news for illegal immigrants who have been waiting, in some cases for years, for legal status.

“This bill is not perfect, but it’s a really good solution, in my view, to a very difficult problem,” said Sen. Lindsey Graham, a South Carolina Republican who was part of the bipartisan “Gang of Eight” senators who wrote the bill and managed to fend off every major challenge to it.

Now the fight shifts to the Republican-led House, where Speaker John A. Boehner once again insisted that the Senate bill is dead on arrival.

“The House is not going to take up and vote on whatever the Senate passes,” the Ohio Republican said flatly at his weekly news conference before attacking the Senate version as too weak on border security.

Instead, Mr. Boehner seemed to sketch out a path that would put a series of smaller bills on the chamber floor, rather than the broad approach the Senate took, which mixes legal immigration, enforcement and the status of 11 million illegal immigrants into a 1,200-page bill.

Senate supporters of legalization said they hoped Mr. Boehner would rethink his strategy, though they fell just shy of the 70-vote threshold that they said would create the momentum to force the House to act.

President Obama, traveling in Africa, issued a statement praising the Senate vote while warning that it still faces an uncertain future.

“Now is the time when opponents will try their hardest to pull this bipartisan effort apart so they can stop common-sense reform from becoming a reality,” Mr. Obama said. “We cannot let that happen.”

Sen. John McCain, Arizona Republican, said other Republicans supported the bill but didn’t vote for it, though he didn’t say who they were. But he said getting to 68 was a major accomplishment.

“The day we announced this legislation, we were a long, long way from 68 votes,” he said.

He and his fellow Gang of Eight members did a masterful job of holding together and expanding their coalition, in part by denying senators the chance to amend the bill.

Of more than 550 amendments filed, only about a dozen were put to votes, and just one was a major change that passed.

A last-minute effort to approve other changes failed when Republicans objected.

Senators gave the final vote the full pomp of landmark legislation. Majority Leader Harry Reid, Nevada Democrat, asked that senators vote from their desks — a formality reserved for the biggest issues, such as the 2009 vote on Mr. Obama’s health care act. Vice President Joseph R. Biden presided over the session and read out the final vote totals.

“It’s historic,” said Mr. Reid, who is one of the chief reasons the legislation has advanced this year.

It was Mr. Reid’s re-election in 2010 and Mr. Obama’s re-election in 2012 — both aided by strong Hispanic support — that helped put immigration back to the fore of the political conversation.

Since Mr. Obama’s November victory, congressional Republicans have held a fierce internal debate over whether they need to pass a legalization bill in order to compete for Hispanic voters.

The crux of the Senate bill is a deal to offer quick legal status to illegal immigrants, but withhold full citizenship rights until some conditions are met. Backers said they didn’t want to repeat the experience of the 1986 immigration law, when millions of illegal immigrants were granted citizenship but the government never followed through on enforcement, leading to millions more illegal immigrants.

This time, they said, they would tie future citizenship rights to checking off boxes on border security.

But the key point of contention has been over how strict to make those conditions. Democrats have said they don’t want to do anything that would interfere with the path to citizenship, and they have succeeded in beating back amendments to make the citizenship path contingent on provable success. Instead, the Senate bill relies on measures of spending and having infrastructure and manpower in place.

The one major amendment that passed, proposed by Republican Sens. Bob Corker of Tennessee and John Hoeven of North Dakota, called for adding 20,000 Border Patrol agents to the Southwest and would push the Homeland Security Department to build an additional 350 miles of pedestrian fencing.

Mr. McCain said the staffing, infrastructure and technology are the guarantees he needs to be certain the failures of 1986 aren’t repeated.

“I can tell you from 30 years of being on the border, this bill secures the border, and anyone who says it doesn’t does not understand our security needs,” the senator said.

But the National Border Patrol Council, which represents Border Patrol agents, said it had “serious concerns” about the boost in staffing.

“Unless we’re going to form a human chain from Brownsville to Imperial Beach, I’m not sure this is going to be the cure that everybody thinks it will be at the border,” said Shawn Moran, a vice president at the council. “We don’t have money for gas or ammunition or uniforms, and that’s at 21,000 agents. I’m not sure how we’re going to be able to handle 40,000 agents. I don’t know where we’re going to put them.”

The council had a different proposal to reform agents’ pay, which Mr. Moran said would have put more agents into the field and would have been the equivalent of a 5,000-agent boost over the course of a year. But that proposal got held up along with the hundreds of other amendments that never were put to a vote.

In addition to Mr. McCain, Mr. Corker, Mr. Graham and Mr. Hoeven, the Republicans supporting the legislation were Sens. Lamar Alexander of Tennessee, Kelly Ayotte of New Hampshire, Jeff Chiesa of New Jersey, Susan M. Collins of Maine, Jeff Flake of Arizona, Orrin G. Hatch of Utah, Mark Kirk of Illinois, Lisa Murkowski of Alaska and Marco Rubio of Florida.

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