(Adds Pence comment, paragraph 6)
By Susan Cornwell
WASHINGTON, Feb 2 (Reuters) - Republicans in Congress struggled on Thursday with their efforts to dismantle Obamacare, with conservatives urging haste while some lawmakers said the task had become more of a repair job than the repeal of the U.S. healthcare law promised by President Donald Trump's administration.
Two influential conservatives in the House of Representatives, worried that the process was getting bogged down, said the repeal measure that the Republican-majority Congress passed last year should be taken up quickly.
But in the Senate, Republican Lamar Alexander of Tennessee and chairman of the health committee counseled patience. He said changes to the law would be made in "chunks" and would be better labeled a "repair."
"It's more accurate to talk about repairing it ... we're repairing the damage Obamacare has done," Alexander said outside the Senate.
"We're not repealing all of Obamacare, it's not technically possible to do that (now) in the procedures that we have in the Senate, and secondly, there are some parts of it we want to keep," he said.
But Vice President Mike Pence, asked in a Fox News interview about talk of repairing Obamacare, pushed back, saying: "We are absolutely committed to follow through on President Trump's directive to repeal and replace Obamacare and to have the Congress do it at the same time."
Trump and congressional Republicans campaigned on a promise to dismantle the 2010 Affordable Care Act, former President Barack Obama's signature domestic legislation that Republicans consider federal government overreach.
While Republicans voted last month to start the process of scrapping the law, they missed a target date of Jan. 27 to begin drafting legislation to do so. At a congressional retreat last week, Republican leaders told lawmakers they hoped Congress would finish the repeal by March or April.
Representative Mark Meadows, chairman of the conservative Freedom Caucus, and Representative Jim Jordan, the caucus' former chairman, urged the party leadership on Thursday to quickly enact a repeal measure.
"That's what the American people expect us to do - and they expect us to do it quickly," they said.
Obama, a Democrat, vetoed the repeal passed by the Republican-controlled Congress last year.
Three of the biggest national insurers have also stepped up pressure on the lawmakers to act. Aetna Inc, Anthem Inc and Cigna Corp this week urged changes in Obamacare individual plan regulations in the next few weeks, in time for them to decide if they will sell the products in 2018.
They want stricter oversight of eligibility and enrollment periods, as well as other changes. Without them, these insurers say they may pull out of the Obamacare exchanges next year, which would lead to less competition and higher premium rates. Rates for 2017 rose an average of 25 percent.
Edmund Haislmaier, a Heritage Foundation senior research fellow who advised the Trump transition team to help craft the regulation change but has not seen the final version, said he expected it to address concerns of insurers. He said insurers were consulted.
"The incoming administration and the insurers have by in large the same agenda on a lot of this stuff," said Haislmaier.
He said that pleasing the insurers could help Congress move more quickly on a plan to repeal and replace the law.
"The (administration) can reassure Republicans that we're taking steps so the market doesn't blow up when you move ahead with legislation, and I think that would actually maybe move the process along on the Hill," he said.
Democrats were enjoying the Republican turmoil. They have long accused Republicans of rushing to gut the law without having a replacement plan ready. The law has enabled up to 20 million previously uninsured Americans to obtain health coverage.
"They (Republicans) haven't come up with the so-called repairs," the Senate's No. 2 Democrat, Dick Durbin of Illinois, said in a hallway. "What a departure (for the Republicans), from 'let's repeal it and walk away from it and America will be a better place.'" (Reporting by Susan Cornwell; additional reporting by Eric Beech, Ginger Gibson and Caroline Humer; editing by Tom Brown and Grant McCool)