WASHINGTON (Reuters) - The U.S. House of Representatives will resume action next week on repealing President Barack Obama's landmark healthcare overhaul, a House Republican spokesman said on Thursday.

The House had been expected to act this week on the repeal bill, but the vote was postponed after a shooting spree in Arizona killed six people and critically wounded U.S. Representative Gabrielle Giffords.

"As the White House noted, it is important for Congress to get back to work, and to that end we will resume thoughtful consideration of the health care bill next week," said Brad Dayspring, a spokesman for House Majority Leader Eric Cantor.

"Americans have legitimate concerns about the cost of the new healthcare law and its effect on the ability to grow jobs in our country," he added.

The vote is set for Wednesday, said another Republican aide who asked not to be identified.

The repeal vote would fulfill a campaign promise of Republicans who won control of the House in November elections. But the measure will likely die in the Senate, where Democrats remain in control.

Even if repeal were to pass the Congress, Obama would veto it, the White House has said.

Conservative Tea Party activists, who were crucial to Republicans winning control of the House and picking up seats in the Senate, deride the healthcare law as one more government intrusion on the heels of Washington's bailout of troubled banks and the automotive industry.

The House is also expected to vote on a second measure that would instruct three House committees to develop replacement healthcare legislation that would, among other things, "foster economic growth and private sector job creation by eliminating job-killing policies and regulations."

Democrats argue the healthcare overhaul that was signed into law last year will expand coverage to millions of uninsured Americans and help rein in soaring medical costs. But Republicans argue the coverage mandate in the legislation is unconstitutional and that penalties for employers who do not provide coverage discourage hiring.

Some parts of the law already have gone into effect, with more set to roll into place over the next four to five years.

The Congressional Budget Office has said that repealing the legislation would add $230 billion to budget deficits over the next decade. But Republicans have largely dismissed that estimate, arguing that the assumptions are flawed and that over time the healthcare law would deepen deficits.

There are widespread concerns over long-term U.S. debt burdens. The rising cost of government healthcare programs is a major factor in the accumulating red ink.

The battle over the healthcare law is also being waged in U.S. states, who are charged with implementing many of its key requirements. On Tuesday, Kansas took the first step in joining a multi-state lawsuit led by Florida, saying the reforms are an overreach of federal power.

Currently, more than half of all states are suing, and the U.S. government is appealing a recent decision by a federal judge that the law's requirement all individuals have health insurance or pay a fine is unconstitutional.

(Additional reporting by Lisa Lambert; Editing by Doina Chiacu)