Clinton's failed efforts after his 1992 election to create universal health care — with an initiative led by then-first lady Hillary Clinton — helped spur historic Democratic losses in the 1994 midterm elections and doomed the president to years of bitter battles with an opposition Congress.
Obama succeeded in getting his health-care reform passed on party-line votes but Democrats also lost control of the House following massive defeats in the 2010 midterms and lost ground in the Senate. Obamacare advocates believe the program's implementation was well worth the political price.
Trump could be headed for similar trouble, though Republicans appear to have a firmer grip for the moment on the House. And the GOP has a very favorable Senate map in 2018. Many political analysts expect Republicans to expand their majority in the upper chamber next year.
But health care has a way of scrambling existing political certainties.
Even some conservative Republicans now appear to see major risks associated with repealing a health-care law that has extended coverage to more than 20 million Americans without having an immediate replacement that would ensure people don't lose their insurance while keeping some of Obamacare's more popular provisions, like forbidding insurers from excluding pre-existing conditions.
Five Republican senators on Monday — Bob Corker, Rob Portman, Susan Collins, Bill Cassidy and Lisa Murkowski — submitted an amendment to the Senate budget bill that would extend the deadline for crafting an Obamacare replacement into March. Other influential GOP senators including Lamar Alexander of Tennessee and Rand Paul of Kentucky have also said they want a replacement bill ready before major provisions of the Affordable Care Act are repealed.
Trump also seems to support the idea of repealing Obamacare and replacing it at the same time. He will undoubtedly be asked about his plans during his much-anticipated news conference on Wednesday. And Republicans on the Hill will likely be guided in their approach by whatever Trump says.
But there are political risks for Trump in waiting for a replacement bill as well. The Republican base loathes Obamacare — though less so if you take the outgoing president's name off of it — and expect the new president to preside over an immediate evisceration of the outgoing president's signature achievement. So Trump has to deliver. But he doesn't want to be known as the president whose first act was to snatch away affordable insurance from millions of Americans.
It's a highly complex and politically fraught dance. If it goes badly, Trump could wind up facing the same kind of midterm blowback that dogged Clinton and Obama. He needs Republicans to quickly settle on an Obamacare replacement that essentially rebrands the law, doesn't kick people off existing plans and yet still somehow lowers costs and improves coverage.
It's not clear such a thing is even possible. So Trump could find himself the latest in a line of presidents whose efforts to reshape the American health-care system wind up costing them dearly at the ballot box.
—Ben White is Politico's chief economic correspondent and a CNBC contributor. He also authors the daily tip sheet Politico Morning Money [politico.com/morningmoney]. Follow him on Twitter @morningmoneyben.