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A legalization bill passed the Senate in 2006 but stalled as the House went in the other direction, passing an enforcement-only bill that drew millions into the streets to protest. The Senate tried again a year later, but a bipartisan filibuster blocked the bill.

Lawmakers said the issue bedevils them because it pits two fundamental American values against each other: the rule of law versus a history as a nation of immigrants.

That history of immigration played a major role in Thursday’s debate.

“I remember today, my mother, who came to this country with a dream, not knowing the language, not having anybody here to receive her and taking a chance on that dream, a chance that ultimately led to having her son serve in the United States Senate and to be here on this historic day,” said Cuban-American Sen. Robert Menendez, a New Jersey Democrat who voted for the bill.

But for Mr. McConnell, a Kentucky Republican, his vote was informed by the experience of his wife, Elaine L. Chao, who arrived in the cargo hull of a ship from Taiwan at the age of 8 not knowing any English, and decades later was being sworn in to the Cabinet as labor secretary.

“This is the kind of story that has made this nation what it is. Legal immigration made it possible,” Mr. McConnell said.