WASHINGTON — Congress opened for battle over the Affordable Care Act on Wednesday as Republicans pushed immediately forward to repeal the health care law and President Obama made a rare trip to Capitol Hill to defend it.

The bitterness that has long marked the fight intensified as Republicans seized the opportunity to make good on a central campaign promise to get rid of the law, a pledge reinforced on Wednesday by Vice President-elect Mike Pence, who met with House Republicans not far from where the president gathered with Democrats.

The Affordable Care Act, Mr. Obama’s signature health care law, has created online insurance marketplaces, offered new protections to people seeking health insurance, and provided coverage to millions of people near the poverty line through expanded Medicaid. Health policy experts say that system could collapse if Republicans cut off funds for the expanded coverage and end penalties for people who go without health insurance.

“The American people voted decisively for a better future for health care in this country,” Mr. Pence said, “and we are determined to give them that.” He said that President-elect Donald J. Trump would use his executive authority to help make the transition away from the health care law, but did not offer specifics.