The initial round of debate Tuesday was free of the rancor seen during the sessions that culminated in party-line passage of the historic legislation in 2010.
The law would provide coverage to more than 30 million uninsured people, with tax credits to make premiums more affordable for the middle class, along with an expanded Medicaid program for the poor.
Starting in 2014, most Americans would be required to carry health insurance, a first-of-its-kind mandate that Republicans are challenging as unconstitutional in federal court.
The Associated Press contributed to this report.