When it comes to the feud between Sen. Rand Paul (R-Ky.) and New Jersey Gov. Chris Christie (R), it's Christie who's fighting an uphill battle -- at least if both run for president in 2016.

Newly released numbers from the Pew Research Center show that, in a poll conducted before their spat over surveillance programs, Paul had significantly better approval numbers than Christie.

While 55 percent of Republicans and GOP-leaning independents had a favorable view of Paul in mid-July, 19 percent had an unfavorable one. These voters were much more split on Christie, with 47 percent favorable and 30 percent unfavorable.

Those numbers among Republicans and GOP-leaning independents are actually not very good for Christie, given this is his party's base. But much of his popularity right now is bipartisan -- a reflection of his willingness to associate with President Obama and sometimes buck the conservative wing of the GOP.

Perhaps more interesting is that, even before the current battle between the two men, those concerned about the NSA's surveillance programs were significantly more supportive of the libertarian-leaning Paul, while those who tended toward national security backed Christie.

Those who disapproved of the NSA's programs liked Paul by a 61-18 margin, while those who approved of them liked Christie 56-25.

The lesson: While Christie suggested Paul was using him to gain media attention, it's actually Paul who was in better position with Republican voters when the back-and-forth ensued.

As for who is helping himself in the current feud, only time (and future polls) will tell.