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CHICAGO - With Ron Paul looking more and more like a legitimate threat to win the Iowa caucuses in two weeks time, the libertarian Republican candidate is coming under fire from those in his party for differences on key policies.

At a campaign event in New Hampshire Monday night, a Manchester woman went after Paul for his proposal to eventually eliminate Medicaid and Medicare, with the suggestion that charity hospitals would then help the uninsured.

"Thirty three percent of the children in the U.S. are on Medicaid and another 10 percent are uninsured," the woman said. "You have offered charity by doctors as a solution to this. Do you really think that 43 percent of America's children will be taken care of by charity?"

The woman's questions led to an acrimonious back-and-forth in which Paul at one point acknowledged that his proposal might seem "cold-hearted," but it is simply an effort to save the nation from financial disaster. On Tuesday another audience member in New Hampshire engaged in a testy exchange with Paul over his opposition to a same sex marriage amendment.

Paul's record is coming under fresh scrutiny as a result of the added attention that he is now receiving, both from his rivals and the media, since a Paul victory in Iowa now appears to be a decent possibility. In recent weeks candidates have struggled to take a stranglehold on the race there. Mitt Romney can't get traction, Newt Gingrich has started to slip, Rick Perry surged in the summer but then slumped, Michele Bachmann won the state's straw poll only to later plunge in the polls, and Herman Cain suspended his campaign.

Read the latest ABC News / Washington Post Poll, which places Paul solidly in third place among Republicans nationwide. He is thought to have more support in Iowa.

But someone's got to win this thing and, more and more, signs in the Hawkeye State suggest that someone could be Paul.

With Gingrich fading and Romney seemingly stuck at the same levels of support he has enjoyed for the past six months, the door is open for Paul to spring a surprise in Iowa. The Texas congressman, whose backers might be the most vocal and loyal of any in the race, leads Romney by a 2-to-1 margin as the candidate most likely to "stand up for what he or she believes."

"The challenge isn't all that great on how we're going to beat Obama. I think he's beating himself," Paul said at Thursday's debate in Sioux City. "I think really the question is, what do we have to offer? And I have something different to offer. I emphasize civil liberties. I emphasize a pro-American foreign policy, which is a lot different than 'Policemen of the World.' I emphasize, you know, monetary policy and these things that the other candidates don't talk about.

"But I think the most important thing is the philosophy I'm talking about is the Constitution and freedom. And that brings people together. It brings independents into the fold and it brings Democrats over on some of these issues. So therefore I see this philosophy as being very electable because it's an America philosophy."

But the electability question is one that has plagued Paul. While he has earned the fervent devotion of his supporters by standing out from the crowd, his critics contend that he has no shot of earning the GOP nomination and, if somehow he did, the consequences would be disastrous for the party. At a debate last Thursday, for instance, Paul declared that even if there were proof that Iran had obtained a nuclear weapon, he would still not engage in another war in the Middle East, a stance in stark contrast to that of most other Republicans. At another point in the debate, he referenced Austrian economists in denouncing Gingrich for his role in the United States' housing bubble.

"What would happen if Ron Paul won the Iowa caucus? The results would become totally insignificant, we would lose our first-in-the-nation status, and Mitt Romney would waltz to the GOP nomination," Kevin Hall wrote on TheIowaRepublican website last week.

"To be blunt," added Tim Hagle, another one of the website's contributors, "Paul's foreign policy and national security positions are considered too extreme for most of the GOP base. Many can overlook them when the focus is on fiscal issues, but Paul got a lot of air time in the last debate …"

Hagle cited one potential stumbling block for Paul in Iowa: his popularity among younger voters aged 18-25 could prove problematic because those voters are the least likely to attend a caucus and vote, and colleges will be on break when the caucuses take place Jan. 3.

But Paul, 76, also boasts great organization in Iowa and, as opposed to other candidates such as Romney and Gingrich, he has logged countless hours on the ground there. In addition, he only lost the Ames straw poll to Bachmann by a mere 152 votes.

Since the straw poll started in 1979, the candidate who has gone on to win the caucus had placed first or second in Ames every time. After the straw poll in August, it appeared that Bachmann might run away with the evangelical vote and emerge as the favorite to win Iowa, but evangelicals have yet to coalesce around a specific candidate, Bachmann has faded, and it is Paul who has continued to climb up the polls.

"Dr. Paul is surging in Iowa and New Hampshire because he is exactly what the voters have been looking for," Paul spokesman Jesse Benton said in an email. "He governs on principle. He is consistent and does not flip-flop. And he is the only candidate who will really cut the spending and balance the budget so we can get back on our feet and create jobs."

Matthew Jaffe is covering the 2012 campaign for ABC News and Univision.