The core tenet of conservatism in its modern form is an opposition to taxation for the purpose of redistribution to the poor. The core purpose of Obamacare was to provide healthcare to people who couldn't otherwise afford it, and the only way to pay for that was through taxation following the Willie Sutton rule. Willie Sutton was a bank robber. When asked why he robbed banks, his answer was simple. That's where the money is. Why do Democrats want to tax the rich? That's where the money is.
So, Republicans now find themselves in a rhetorical bind. For years, they have been promising to "repeal and replace" Obamacare. The problem is that "replace" indicates dissatisfaction with the pre-Obamacare status quo. Yet, that system was not one that Republicans, or at least conservative Republicans were eager to change. Every time Democrats got a chance, they made moves to change the healthcare system, by trying to expand healthcare coverage, at cost to someone. They failed, until 2010. The most famous failed attempt was the Clinton attempt during 1993-4, and that should be striking because after 1994, the next time Democrats had unified control of government was... 2009! So, basically, any time Democrats had a chance, they tried healthcare reform. They didn't succeed until 2010, which was when they had a big majority in both houses of Congress, and relatively liberal voting blocs in each (all the Southern Dems were gone).
How about unified Republican control? Well, much of George W. Bush's Presidency was unified. Did they attempt major healthcare reform? Um, no. Other than that, it is a little tough because before W, you have to go back a long way for another unified Republican government. But, there was Reagan's nearly unified first six years (he had the Senate), and they didn't do bupkis. Why? If you oppose redistribution on principle, then why would you have the government intervene to create a welfare program?
Conservatism in its modern form opposes redistribution. The reason that the Republican Party is struggling with the "replace" part of "repeal and replace" is that they don't want to replace a redistributive policy. This is a party trapped by its own bullshit rhetoric.