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Republicans are wasting no time in their effort to repeal Obamacare.

Senate Republicans took the first official step toward repealing President Barack Obama's signature healthcare law Tuesday afternoon, filing a budget resolution that puts the wheels of overhauling the Affordable Care Act into motion.

The move, coming just hours after the commencement of a new session of Congress, underscored that stripping down Obamacare will be the Republican Party's top legislative priority under future President Donald Trump.

The Senate debate over the resolution is expected to take multiple days, likely dragging out into next week, according to a Senate GOP source. Democratic lawmakers could also try to slow down the process by proposing numerous amendments.

The budget resolution is the first in a two-part process to repeal Obamacare. It instructs relevant congressional committees to craft a budget reconciliation bill, which will include language repealing major parts of the law.

Congressional sources say the process of crafting the reconciliation bill could take weeks, and a vote on that bill may not take place until February or later.

Republican lawmakers have dubbed the budget resolution the Obamacare "repeal resolution" to emphasize its purpose of repealing the law.

In a statement, Republican Senate Budget Committee chairman Mike Enzi said the GOP is set on fixing a "broken" national health care system.

"Americans face skyrocketing premiums and soaring deductibles," Enzi said. "Insurers are withdrawing from markets across the country, leaving many families with fewer choices and less access to care than they had before -- the opposite of what the law promised."

Broad legislation to repeal and replace Obamacare would require 60 votes in the Senate, and Republicans don't control enough seats to make that happen or to squash a filibuster by the Democrats.

Instead, Republican lawmakers are expected to use the budget process, which is limited to provisions that affect federal revenues and spending and requires only a simple majority to pass. It would enable Congress to repeal the Obamacare mandates that individuals have coverage and that companies with 50 or more employees provide workers with affordable insurance. Also, it can do away with the federal subsidies, eliminate funding for Medicaid expansion and cancel a multitude of Obamacare-related taxes.

The urgent question Republicans must grapple with now is how they will go about replacing what they repeal.

Republican leaders are considering a "repeal and delay" approach of preventing the repeal from going into effect for two or three years. This transition period would buy lawmakers some time to figure out a replacement plan, but already, insurance companies are balking at the uncertainty that this scenario would create.

GOP Sen. Lamar Alexander, the chairman of the Senate Health Committee, has gone as far as to say that it would be a mistake to repeal Obamacare before Republicans craft a replacement.