WASHINGTON  Handing President Obama a hard-fought victory, the House narrowly approved a sweeping overhaul of the nation’s health care system on Saturday night, advancing legislation that Democrats said could stand as their defining social policy achievement.

After a daylong clash with Republicans over what has been a Democratic goal for decades, lawmakers voted 220 to 215 to approve a plan that would cost $1.1 trillion over 10 years. Democrats said the legislation would provide overdue relief to Americans struggling to buy or hold on to health insurance.

“This is our moment to revolutionize health care in this country,” said Representative George Miller, Democrat of California and one of the chief architects of the bill.

Democrats were forced to make major concessions on insurance coverage for abortions to attract the final votes to secure passage, a wrenching compromise for the numerous abortion-rights advocates in their ranks.