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By Andrew Rafferty

Vice President-elect Mike Pence on Wednesday called for a swift but “smooth” repeal of the Affordable Care as President Barack Obama visited Capitol Hill in the hopes of protecting his signature legislative achievement against a GOP agenda set on dismantling it.

"The first order of business is to repeal and replace Obamacare, and that was our message today and that will be our message on Capitol Hill," Pence told reporters after meeting with Congressional Republicans.

Ahead of Pence's press conference with Congressional leadership, the president-elect went on a Twitter rant blaming Democrats for "massive increases" in premiums and saying the law will "fall of its own weight."

Simultaneously, Obama visited lawmakers on Capitol Hill to urge them to defend the law that has provided 20 million Americans with insurance.

“He said, 'Listen, don't mistake my cool demeanor for a lack of outrage. I'm angry just like you are about what has happened in the election and after the election.' And I think you could sense that he, you know, is maybe feeling a little forlorn that he's not going to be in this fight in the way that we are,” Democratic Sen. Chris Murphy said on MSNBC after the private meeting.

Related: Replacing Obamacare Will Be Difficult, Repealing It Could Be Just as Hard

Another source in the room said the president lamented that he will soon be a private citizen because “I would love to be on the field.”

Republicans began what is expected to be an arduous process of following through on repealing and replacing Obamacare the same day a new Congress was sworn in. Though the GOP will soon control the White House, Senate and House of Representatives, they have yet to rally behind a single replacement plan.

Pence signaled the first steps the GOP will take is continuing to make the case against the Affordable Care Act, which Democrat Hillary Clinton also pledged to modify during the 2016 campaign.

And while calling Obamacare’s repeal a top priority for the incoming Trump administration, Pence also cautioned that lawmakers must ensure an "orderly and smooth transition" to a new healthcare system before full repeal.

"It will be important that we be careful that ... we do that in a way that doesn't work a hardship on American families that have gained insurance through this program. That it doesn't work a hardship on this economy," Pence said.

House Speaker Paul Ryan also said Republicans don't want to "pull the rug out from people."

Senate Minority Leader Chuck Schumer said Republicans are like “the dog that caught the bus" — able to repeal Obamacare but not sure how to replace it.

“Republicans say repeal and replace. The only thing that has going for it is alliteration,” House Minority Leader Nancy Pelosi said. “They have no replacement plan.”