The movement to draft Massachusetts Senator Elizabeth Warren into the Democratic race for the presidency has always faced two big challenges:

1. Warren says she is not running.

2. Warren trails far behind Hillary Clinton in the polls of voters in the first caucus state of Iowa and the first primary state of New Hampshire. Nationally, the Real Clear Politics average of recent polls puts Clinton at 60 percent. Vice President Joe Biden in in second with 11.4 percent. Then comes Warren with 11.1 percent and Vermont Senator Bernie Sanders with 3.4 percent.

The point of the draft movement is to get Warren to address challenge No. 1 by changing her “no” to “yes” and entering the contest. But that change is unlikely to occur if challenge No. 2 is not addressed by polling that suggests a Warren run would be welcome and viable.

So the “Run Warren Run” draft campaigners hired the YouGov polling organization to survey likely Iowa Democratic caucus goers and New Hampshire Democratic primary voters. What the polling reveals is that

1. Likely Democratic voters in both states want to see a contest for the Democratic nomination. According to the memorandum analyzing the data, “Virtually all respondents agree with the case for a contested race, with 98% agreeing that a competitive primary is good for the party, candidates and voters.”

2. When likely Democratic voters are presented with information about Warren and her populist positions on the issues ranging from trade policy to banking regulation to student loan debt, they become more enthusiastic about her running—and about backing her in a race that also includes Clinton. Indeed, while a plurality of likely voters remains undecided in each state, Warren moves into a credible lead over Clinton in Iowa (31-24, with 6 percent for Sanders) and a narrower lead in New Hampshire (30-27, with 6 percent for Sanders).

This sort of polling can be instructive, but it is far from definitional.

First off, there’s a need for a big note of caution with regard to those horse-race numbers. By presenting positive information about Warren, the survey creates some balance for the advantage Clinton enjoys because of high name recognition and high approval ratings among Democrats. It gets voters thinking. That’s reasonable, since it is fair to assume that a Warren campaign would seek to do just that. But there are no guarantees that campaigns go according to plan, or that other candidates will not counter those campaigns with their own positive and negative messages. In other words, these numbers point to possibilities as opposed to providing anything akin to assurances.

The analysis of the Iowa and New Hampshire polling data distributed by key groups backing the draft effort— Political Action and Democracy for America—frankly notes that “this is not a so-called ‘clean’ head-to-head ballot question, as voters were provided positive information about Warren but not other potential candidates. It should not be read as reflecting how Iowans or Granite Staters would vote if the caucuses or primary were held today. Rather, it should be read as an indicator that many voters in these states are ‘moveable,’ open to supporting Elizabeth Warren when they learn about her, and like what she has to say.”

So it is important to keep the horserace numbers in perspective.

But it is also important to recognize the significance of those numbers regarding the desire of Democrats for a contest. That is strikingly evident not just from the polling data but also from what activists and elected officials have told me on my recent trips to New Hampshire and Iowa.

I was in Des Moines over the weekend, speaking with a number of progressive activists. A number of them were already wearing pro-Warren T-shirts and posting signs backing the senator. Many were also circulating petitions urging Sanders to seek the Democratic nomination and displaying “Run Bernie Run—as a Democrat” stickers distributed by Progressive Democrats of America.

The desire for a debate is real. So, too, is the worry about a caucus and primary season where the Republicans are campaigning, holding debates and getting all the attention while the Democrats barely go through the motions.

Both parties should have wide-open nominating processes, with multiple candidates and—above all—serious discussion of the issues. Republican and Democratic elites might prefer coronations. But the bases of both parties want real competition and real debate. Republicans are already beginning to experience that competition, and Democrats are hungry for it.

As the memorandum analyzing the YouGov data indicates: “Virtually every Iowa caucus goer and New Hampshire primary voter, including those supporting Hillary Clinton in this survey, agrees with this argument in favor of a contested primary: ‘More than one candidate should compete for your support before getting your party’s nomination. It’s good for candidates and the Democratic Party to have to formulate and explain their positions on a range of issues. And it’s good for your state to have multiple candidates who are coming to the state and educating voters about where they stand on the issues.’”