KEOKUK, IOWA (CNN) Sen. Elizabeth Warren has been using new, notable language at her town halls to describe the transition into "Medicare for All" -- saying, under her plan, it would be a voter's "choice" to opt in.

While the language is already a part of her transition proposal, it's a notable rhetorical shift on Warren's part after her moderate Democratic rivals -- namely South Bend, Indiana, Mayor Pete Buttigieg -- have criticized her plan that would eventually eliminate private health insurance.

For the last two weeks, Warren has described the transition into her Medicare For All plan as a "choice" for Americans to try it. A new Fox News Poll released Sunday showed that support for government-run healthcare has dropped by double-digits among Democrats since October.

At her town halls, Warren frequently fields questions from voters who tell her they've heard worries from friends or family about giving up their current private insurance.

During a stop in Keokuk, Iowa, on Monday morning, 54-year-old Camille Anderson told Warren she was a fan of her Medicare for all plan, "but I keep hearing from people who are afraid, (a), of the cost and, (b), that they're not going to be able to get the care they need or see the doctor that they want with your plan. Is there something you can say to alleviate their concerns and their fears?"

After a lengthy explanation of how her plan would work, the Massachusetts senator emphasized to Anderson that she believes Americans will embrace the plan once they see it in action.

"Let's let people try it," Warren said in Keokuk Monday morning. "Find out what it feels like to be making healthcare decisions just between you and your medical professional to get the prescription drugs you need without having to worry about how big the copay is going to be, and whether or not you're going to be able to get the prescription filled and still have enough money left over to buy groceries this week.... When tens of millions of people have had a chance to try that, I believe, at that point, we're going to be ready to vote for Medicare for everyone."

In November, Warren released her transition plan that would implement Medicare for All in two phases. The first would use a Senate budget process to pass legislation that would immediately offer Medicare for All's full suite of benefits -- at no cost -- to children under 18 and people at up to 200% of the poverty level, around $51,000 in income for a family of four.

The option would be open to any American who wants to use it, but they would have to pay for it, though costs would decline over time. Additionally, the legislation would lower the current Medicare eligibility age to 50 from 65, while also expanding the program's benefits and lowering what enrollees have to pay.

In a second phase for the plan, Warren said she would push Congress to pass the full Medicare for All legislation.

When asked about her recent verbal shift during a press availability with reporters Sunday in Ottumwa, Iowa, Warren argued she "is just talking about the plan."

"The plan's been there from the beginning, and I'm just trying to make sure that everyone understands. The part I talk about the most is what I want to see happen -- and that is the most help to the most people as quickly as possible," she added. "That's a choice for everyone to make."

Warren's rhetorical shift may be driven in part by the split within the Democratic Party over how to best handle the health care issue, and the uneasiness among more moderate voters about the difficulties of transitioning to a Medicare for All system. That division has been highlighted in the primary debates; in October, Warren in particular was assailed over Medicare for All and her refusal to directly state how she would pay for it. (Warren went on to release her funding proposal in November .)

In interviews with voters in swing states this year -- particularly in union areas where workers have fought hard for their health care benefits -- many moderate voters have said they cannot support either Warren or Vermont Sen. Bernie Sanders because of their embrace of Medicare for All, which they think would harm the quality of their current benefits and the Medicare system overall.

Some more moderate Democratic voters worry that the controversy over the elimination of private health insurance system would harm the Democrats' chances against President Trump in November.

A new Fox poll released Sunday underscored that concern showing that 53% of all voters are opposed to a government-run health care program; while 66% of all voters favor Medicare for All for those who want it.

Among Democratic primary voters in the Fox poll, 78% said they favored allowing all Americans to buy into the Medicare system. Only 54% of Democratic primary voters said they favored moving to government-run health care -- a figure that fell from a high of 65% in October.

The Fox News poll also found that Warren's support has dropped since late October -- there was a 13-point drop in her support among those with a college degree; a 12% drop among voters over 45; and an 11-point drop among women.

Democrat Chris Anderson, who conducts the Fox News poll with Daron Shaw, attributed part of Warren's drop to the fact that some primary voters have soured on Medicare for All -- because of a recognition that defending the program will be difficult in a general election fight against Trump.

In debates, Biden and Buttigieg have tried to use the uneasiness about Medicare for All to their advantage by making the contrast between their more gradual approach and that of Warren and Sanders. Biden has criticized the cost of Medicare for All as unrealistic, and argued that it would raise taxes on the middle class. He has proposed expanding coverage by building on the Affordable Care Act, which expanded access to healthcare during the Obama administration.

Buttigieg described his plan as "Medicare for All Who Want It," adding at a recent fundraiser: "I'm going to leave it to you to decide whether you want it instead of telling you what's good for you. That's how we get everyone covered."

After Warren's town hall in Keokuk on Monday, Camille Anderson said she was still committed to voting for Warren, but she worries that the Massachusetts senator's explanations of her plan in her answer still may not alleviate concerns that "she wants to give away all this free stuff."

"I feel like she's not getting her message across succinctly enough so that people can understand the trade-off costs versus private insurance," Anderson said in an interview after listening to Warren's answer. "I think breaking it down into bullet points is good. But I still think it's too much information for the average person to listen to before their eyes start glazing over. So I'm concerned. I feel like that is the one issue that she keeps struggling with that just keeps popping up -- and is not going to go away."