A flat-out repeal of the health care law would face a steep hurdle in the Senate, where Democrats still cling to a diminished majority, and would most certainly be vetoed by President Obama. But Representative Fred Upton of Michigan, the incoming chairman of the House Energy and Commerce Committee, said the House action would not be merely symbolic. “If we pass this bill with a sizable vote, and I think that we will, it will put enormous pressure on the Senate to do perhaps the same thing,” Mr. Upton said on “Fox News Sunday.” “But then, after that, we’re going to go after this bill piece by piece.”

Certainly as a political matter, the House debate may be the first battle in the new era of divided government, with each side struggling to present itself as the voters’ voice on an issue that has deeply divided the country.

“Many of the incoming Republican congressmen campaigned on the platform that included repealing Obamacare,” Representative Doug Lamborn, Republican of Colorado, said in an interview. “This was the biggest mistake made by the 111th Congress.”

The repeal effort is part of a multipronged systematic strategy that House Republican leaders say will include trying to cut off money for the law, summoning Obama administration officials to testify at investigative hearings and encouraging state officials to attack the law in court as unconstitutional.

For House Republicans, a repeal vote would also be an important, if largely symbolic, opening salvo against the president, his party and his policy agenda.

“Obamacare didn’t lower costs and does not allow people to keep the care they have if they like it, as the president promised,” said Brad Dayspring, a spokesman for Representative Eric Cantor, Republican of Virginia, the incoming House majority leader. “There will be a straight vote to repeal it prior to the State of the Union,” expected in late January.

Representative Michele Bachmann, Republican of Minnesota, said: “It’s important that we repeal Obamacare as soon as possible because it is already harming the economy and killing jobs. Employers are seeing their costs for providing health insurance skyrocket, and that’s causing them to hold off on hiring and job creation.”