WASHINGTON (Reuters) - Urged on by U.S. President-elect Donald Trump, Republican lawmakers rushing to scrap Obamacare said this week they hoped to make some changes intended to stabilize the insurance market while they work at repealing and replacing the law. The beginnings of a framework outlining what a post-Obamacare world could look like came in the same week that  Congress approved a resolution instructing key committees of both the House of Representatives and the Senate to draft Obamacare repeal legislation by a target date of Jan. 27. The fate of the Affordable Care Act, popularly known as Obamacare, is a high-stakes political showdown between Republicans and Democrats that potentially jeopardizes medical coverage for millions of Americans and risks causing chaos in the health insurance marketplace. The seven-year-old law has enabled up to 20 million previously uninsured Americans to obtain health coverage and helped slow the rise in healthcare spending. But Republicans have called it federal government overreach. “If our general goal is to move decisions out of Washington back to the states, we should be able to make those decisions in the next several months,” a key Republican senator working on the repeal, Lamar Alexander, told reporters outside the Senate this week. In a speech on the Senate floor, Alexander indicated Republicans are eyeing some moves insurers have said would help shore up the insurance plans offered on the Obamacare exchanges. The changes could be done by law or by regulation, Alexander said. Alexander said he favors continuing, at least temporarily, the cost-sharing subsidies that millions of Americans receive with their Obamacare exchange-based plans - a kind of financial assistance that helps keep down the cost of deductibles and co-pays. He advocates adjusting the special enrollment periods that insurers say are sometimes abused by people who wait until they are sick to sign up for insurance. Insurers have long sought changes that would fix this facet of Obamacare to weed out misuse. It would also help the transition to a new system, Alexander said, if individuals could use government premium subsidies to buy plans outside of the Obamacare marketplace. Alexander is chairman of the Senate health committee, one of the committees drafting the repeal legislation. He told reporters he had discussed his ideas with a number of senators and the process was evolving, but stressed it should be gradual, with some changes made by lawmakers and some by the secretary of Health and Human Services after he is confirmed.  Trump has nominated Republican Representative Tom Price for the job. “Certainty is something the insurance industry needs so they don’t abandon coverage,” said Senator Johnny Isakson of Georgia, another Republican lawmaker who has been working on how to stabilize  insurance markets. It was unclear whether lawmakers will reach the ambitious target date of Jan. 27 for drafting repeal legislation. But House Speaker Paul Ryan said on CNN on Thursday that Republicans are moving “as quickly as they can”. The 2010 law, Democratic President Barack Obama’s signature piece of domestic policy, touches almost all parts of the U.S. healthcare system, making its replacement likely to take effect over a number of years, even if lawmakers are trying to draft changes in weeks or months.  