Chris Christie raised some eyebrows, as well as the expectations of potential supporters, in the last couple of weeks as he traded barbs with Kentucky Senator Rand Paul in a clash of potential Republican presidential contenders. But while a new Quinnipiac poll should encourage those who think the New Jersey governor is the ideal Republican candidate in 2016, it also illustrates his biggest problem: fellow Republicans.

The poll measures the popularity of leading members of both parties in which voters were asked to measure their feelings toward them on a scale of 0 (ice cold) to 100 (red hot). Out of a field of 22 Democrats and Republicans, Christie placed first with a 53.1 percent rating, beating out second-place finisher Hillary Clinton, who had 52.1 percent approval. That’s the good news for Christie. The bad news is that when narrowed down to the 23 percent of the sample that identified themselves as Republicans, he slipped from first to eighth, finishing behind most of his leading rivals for the presidency–even a dark horse like Rick Santorum. While those figures don’t doom Christie’s hopes for the GOP nomination—he still scores a 59.8 percent rating among Republicans and also can point to his first-place standing among independents—it does illustrate the problem of being perceived as the most moderate contender in the field in a party with a base that takes a dim view of such a stance.

The survey supplies Christie’s supporters with a powerful argument about electability. The New Jersey governor has a unique appeal that transcends the fans he originally won on the right for his YouTube videos in which he berates liberals and unions and plays the kind of tough-guy blunt politician that voters can’t get enough of. Many on the right may never completely forgive him for hugging President Obama in the week before the election last fall during the aftermath of Hurricane Sandy, but Christie’s ability to appeal to centrists, independents, and even some Democrats could make him a formidable general election candidate. But the fact that he has a 53.2 percent rating among Democrats while no other GOP figure scores higher than 32.9 percent (Marco Rubio) is exactly why a lot of Republicans can’t stand him.

The contrast between Christie’s overall numbers and his also-ran finish among Republicans is not the only interesting tidbit from this poll. The fact that Rep. Paul Ryan is the top-rated figure among Republicans with 68.7 percent might help fuel interest in a presidential run by the party’s 2012 veep candidate. Senator Ted Cruz’s second-place rank (65.6 percent) will also give him a boost. But with that pair and Rubio, Wisconsin Governor Scott Walker, Senator Rand Paul, Jeb Bush, and Rick Santorum also scoring 60 percent or higher, it’s clear that there is no single front runner even if it is obvious that Christie might struggle to win in primaries or caucuses where only Republicans are allowed to vote.

Should Hillary Clinton run, there isn’t much doubt that she will be the Democratic nominee in 2016 and her first-place standing in her party with 77.7 percent exceeds even that of President Obama. What is interesting is that freshman Senator Elizabeth Warren of Massachusetts actually ranks third in popularity with all voters at 49.2, beating out Obama with 47.6 percent. Warren trails only Clinton, Obama, and Vice President Joe Biden among Democrats. Should Clinton not run for some unknown reason, Warren’s ability to galvanize the party’s left-wing base could make her an interesting possibility for a long shot upset.

These numbers give us only the broadest possible view of the battle for 2016, two years before the real battle for the nominations will begin. But they do demonstrate that trying to maintain a balance between general election and primary popularity will be even more difficult for Republicans in 2016 than it was in 2012 and 2008 when the GOP wound up nominating a relative moderate to the dismay of much of their base. Conservatives may be wrong to think that Mitt Romney and John McCain’s relative moderation was the reason Barack Obama beat them both and that 2016 is the year to nominate someone who will appeal to their party’s grass roots. But that conviction is not going to be an easy obstacle for someone like Christie to overcome. If, as I wrote last week, the battle between Christie and some of his rivals on foreign and defense policy issues is a fight for the soul of the party, his apparent ability to win in November may still not persuade many in his party to drop their objections to him.