In reality, "it's way more complex than simply 'repeal and replace.' That's a fun little buzzword, but it's just not accurate," the Republican senator told "Squawk Box."
Before the legislation was implemented in 2010, it would have been fair game to repeal and replace it since nobody would get hurt, Johnson said.
"You didn't have already the tentacles of Obamacare, you didn't already have the damage, the destruction, the harm created by Obamacare driving premiums up, distorting health-care markets and health-insurance markets," Johnson said.
Now, Johnson said, the task is much more daunting, and Republicans will need to turn to Democrats for help in fixing the sweeping law, which as of March 2016 provided coverage for roughly 20 million people.
"My thought process is let's start working with Democrats, let's transition to a system that'll actually work that Democrats are talking about. They want to fix it, let's fix it for the benefit of the American public," Johnson said.
A portion of the act that contains tax and subsidy reforms can already be repealed, the senator said. But Republicans' larger focus is tackling certain health-care market reforms that have caused prices on some parts of coverage to surge, he contended.
"It's the market reforms that on the individual market literally have caused, in Wisconsin, individual rates to double and triple, out-of-pocket maximums to also skyrocket," he said. "That's been, from my standpoint, the real disaster of Obamacare, and ... it's a question as to whether or not we can do that with budget reconciliation."
Budget reconciliation allows lawmakers to propose legislation that changes federal spending, revenues, debt limits, or tax policy with relative ease, as the bills proposed are not subject to Senate filibuster and have a limit to how many times they can be amended.
Johnson said he was unsure that Senate Republicans will be able to push through a controversial budget reconciliation proposal like the one repealing Obamacare with just 51 votes. "We are going to need Democrats to help us," he said.
Earlier Thursday, Wisconsin Gov. Scott Walker told CNBC he hopes the new administration keeps its promises and repeals Obamacare "outright." The Republican governor wants states to have a greater say in a replacement.