As the battle over what should be in the bill to replace the Affordable Care Act continues in Congress, another vital fight is being waged over just what to call the plan.

Whether it’s “Trumpcare,” “Ryancare,” or “Obamacare Lite,” the colloquial titles bestowed upon the legislation to replace President Barack Obama’s signature healthcare law could have an impact when it comes to winning both Congressional and public support.

"Much of politics is about branding, and whoever is able to brand the right moniker usually wins the day," said GOP strategist Jeff Sadosky. "Winning the branding debate will win the political fight."

Much in the way “Obamacare” became a pejorative term used by Republicans, the title given to the GOP’s replacement plan has already become a political lightning rod. And similar to how the Obama White House once struggled with how to refer to its healthcare reform, the Trump administration seems similarly stuck on how to handle the label given to its plan, formally known as The American Health Care Act.

Shortly after Republican Congressional leaders unveiled their healthcare plan late Monday, Democrats swiftly began denouncing the bill by attaching the president’s name to it in the same way Republicans linked Obama to the Affordable Care Act. They held press conferences and blasted out emails warning about the dire impact “Trumpcare” will have.

Senate Minority Leader Chuck Schumer repeated it more than a dozen times in a speech on the Senate floor Wednesday.

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Equally as big of a potential headache for the White House was the reaction from conservative members of Congress, who panned it as “Obamacare Lite” for not aggressively enough changing the country’s healthcare system.

The conservative Club for Growth, meanwhile, dubbed it “Ryancare” because the plan was introduced by House leadership.

Related: GOP Rep. Introduces "World's Greatest Healthcare Plan"

Now the Trump White House is in the delicate position of advocating for the framework of the bill with the keen awareness of the risk that comes with linking the president’s name to a political football.

“I’ll call it ‘Trumpcare’ if you want to, but I didn’t hear President Trump say to any of us, ‘Hey I want my name on that,’” White House senior adviser Kellyanne Conway said in an interview on Fox News Wednesday.

Secretary of Health and Human Services Secretary Tom Price told reporters Tuesday he would prefer to call the bill “Patientcare.”

Similarly, the Obama White House did not initially advocate for the president’s name to become a shorthand for the bill and Democrats in Congress called on members across the aisle to stop using the term, saying it was meant to demean the president. Republicans did not pump the brakes and successfully painted Obamacare as a large-scale government takeover that resulted in the GOP winning a mammoth 63 seats in the House in the 2010 midterm elections. But when gearing up for his re-election campaign, Obama signaled to Democrats it was OK to embrace the link between his name and his healthcare plan.

“I have no problem with folks saying Obamacares. I do care,” he said at a town hall in Minnesota in 2011. “If the other side wants to be the folks who don’t care, that’s fine with me.”

Polling shows just how important the name can be. The Affordable Care Act is more popular now than it was during Obama’s presidency, according to an NBC News/Wall Street Journal poll released last month. But despite healthcare being a dominant issue both in Congress and in the past two presidential campaigns, a number of Americans do not seem to understand that the ACA is the same as Obamacare.

Related: Was It a Mistake to Embrace the Name 'Obamacare'?

A poll by Morning Consult in January found 35 percent of respondents either thought the Affordable Care Act and Obamacare were different or weren’t sure. And a 2014 Marist poll conducted for NBC News found that while 57 percent of registered voters in Kentucky had an unfavorable view Obamacare, the approval raised dramatically when asked about “kynect,” the state exchange created by the Obama healthcare law. A plurality of Kentuckians, 29 percent, said they had a favorable opinion of kynect while 22 percent viewed it unfavorably.

The confusion has even been the subject of late-night comedians. Jimmy Kimmel did a skit in 2013 where he asked people on the street to weigh the merits of the Affordable Care Act against Obamacare.

That’s why members of both parties may be looking to Republican Rep. Pete Sessions for inspiration, at least when it comes to naming new legislation. Last week he introduced a reform bill called “World’s Greatest Healthcare Plan of 2017.”