CNN Town Hall Senator Kamala Harris 
Live from Iowa 
Moderated by Jake Tapper
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(CNN) —  

Most Americans want a version of Medicare for everyone, which is good news for presidential candidate Sen. Kamala Harris and other Democrats who support “Medicare-for-all,” a national health care proposal in which people would get their insurance from a single government plan.

But there is an enormous catch: Not all Medicare expansion plans are the same and there is more support for some than for others.

Harris spoke in Iowa on Monday about embracing Medicare-for-all, even though in most instances it means eliminating private insurance. When pressed by CNN’s Jake Tapper on whether that means eliminating private insurance, the senator from California answered affirmatively, saying she would be OK with cutting insurers out of the mix.

That could end up being a sticking point for a lot of Americans.

While a majority of Americans strongly or somewhat favored Medicare-for-all (56%) when they were asked about it in a Kaiser Family Foundation poll from January, significantly more (74%) favored creating a national government-administered health plan similar to Medicare that allows people to keep the coverage they have if they prefer it.

Nearly half of Republicans (47%) are in favor of creating a national government-administered health plan if it allows people to keep their coverage, compared with only 23% of Republicans who favor Medicare-for-all as it is, a form of single-payer health insurance. A little over half (53%) of independents favor Medicare-for-all.

In fact, after being told that a Medicare-for-all plan may eliminate all private health insurance companies, only 37% of all Americans still favored the proposal and 58% opposed it, according to the Kaiser poll.

Most people don’t think that Medicare-for-all means they would have to give up their current insurance: Fifty-five percent said they thought they would be able to keep their insurance under such a plan, and just 35% said they wouldn’t.

Most people (77%) understand that the plan would result in higher taxes.

Around half of registered voters (47%) said in a September NBC/WSJ poll that they would be more likely to vote for a candidate for Congress who favors Medicare-for-all (defined in this case as “a single payer health care system in which all Americans would get their health insurance from one government plan that is financed in part by taxes”).

But Democrats still aren’t sure how to proceed. Around half (47%) of Democrats and Democratic-leaning independents said Democrats in the House should focus on improving and protecting the 2010 Affordable Care Act, while the other half (44%) wanted to focus on passing a national Medicare-for-all plan, from the Kaiser poll.