Republicans make repealing Obamacare 'first order of business'

* Senate opens debate on resolution beginning repeal process

* Pence sees legislation and executive action

* Senate Democrat: Republicans will "make America sick again" (Adds messaging battle between Democrats and Republicans, background)

By Susan Cornwell and Richard Cowan

WASHINGTON, Jan 4 (Reuters) - President Barack Obama exhorted fellow Democrats on Wednesday to preserve his legacy-defining healthcare law as Republicans moved ahead with their long-sought bid to scrap it in what Vice President-elect Mike Pence called the "first order of business" of Donald Trump's administration.

The emerging Democratic strategy is to warn that Republicans risk throwing the entire U.S. healthcare system into chaos by moving to dismantle the 2010 Affordable Care Act, popularly known as Obamacare, without a plan to replace it.

Republicans argue the system is already broken and that they will help more people gain coverage by repealing the law while working to minimize disruptions to those who depend on it.

Both Obama and Pence visited Capitol Hill for closed-door discussions on Obamacare.

Pence, the Indiana governor and a former member of the U.S. House of Representatives, met Republican lawmakers to plot the path forward on scuttling the law.

"The first order of business is to keep our promise to repeal Obamacare and replace it with the kind of healthcare reform that will lower the cost of health insurance without growing the size of government," Pence told a news conference.

Down the hall from Pence, Obama, who hands over the presidency to Trump on Jan. 20, urged Democratic lawmakers to protect his signature domestic policy measure. He told reporters his message was: "Look out for the American people."

Democrats acknowledge they lack the votes needed to stop repeal legislation being pushed by Republicans, who will control the White House and both chambers of Congress when Trump takes office. But they are warning of the risks of the repeal legislation in hopes of spurring a public backlash against it.

Without a replacement by Republicans, as early as 2018, the roughly 20 million people who gained insurance under the law could see their coverage in jeopardy.

"The Republican plan to cut healthcare wouldn't 'make America great again,'" Senate Democratic leader Chuck Schumer told reporters, invoking Trump's campaign slogan. "It would make America sick again and lead to chaos instead of affordable care."

Since the law was enacted, Republicans in Congress have voted more than 50 times to try to repeal all or part of it and conservatives have filed suits to try to invalidate it.