Are there native-born Spanish speakers that can't trill their R's?

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Certainly, there are Spanish native speakers who can't roll the r, but this is not a common problem and rarely represents a difficulty to children.
According to logopedics (logopedia) — the study, and correction, of speech defects, especially in children —, this is called "rotacismo" or "dislalia del fonema r".
Dislalia is classified as a speech disorder. It sounds very weird to native Spanish speakers and according to logopedists it can lead to low self-esteem, social isolation and even statter.
If you allow me to add a personal anecdote here, I've only heard a handful of native speakers having difficulties to roll the r in my whole life, and in this particular moment I can't even remember a person among friends, relatives, students, teachers, colleagues etc... who has this problem.
Please note that even if there are regions where the r is not rolled (some evidence here would be welcome) does not invalidate this truth: that not being able to roll the r in the same way as the rest of the population is a rare phenomenon and of course considered a speech impediment, which can most of the times be corrected by a logopedist.
Please also note that rolling the r is not exclusive to Spanish. Other languages, such as Russian, Polish and German as spoken in Bavaria, roll the r in (nearly) the same way. The same that we are discussing here applies to those languages.
Yes, there are. This whole advertising campaing was based on that. It's one of the most remembered campaings in Argentina and "tapa rosca" has since become a nickname for someone who can't thrill the R here.
Some native Spanish can't trill their R's properly, but I wouldn't say this is a big impediment. As long as there aren't many Rs in a row, such as in "Erre con erre guitarra", this shouldn't be very important.
Regional differences don't really address the original question, because children in those regions learn how to speak as the people around them do, barring any speech defects. But just to add to the list, in Puerto Rico, the RR is guttaral like a French R and not trilled. And in central Peru the RR is frequently pronounced as what a linguist described as a "voiced retroflex fricative", a phoneme I have heard nowhere else on earth.
Are you talking about the Spanish "ere" or the Spanish "erre"? There are some English speakers who can imitate the "ere" passably well, but get all tongue tied when they try to pronounce an "erre".
If you listen to Irish singers, like Celtic Woman or Celtic Thunder, you'll find that Gaelic uses an "R" that is much like the Spanish "ere". So do most dialects of German or Italian. There are undoubtedly other languages that do this. I even think I hear an occarional "erre" in Gaelic, but I'm not sure.
English speakers have a hard time with this sound in any of those languages, including Gaelic, or English with an Irish regional accent. You have to move your tongue in a different way. When you are three years old, learning to do this comes naturally. By the time you are 23, it doesn't come naturally any more. At age 13, when a lot of English speakers start learning Spanish, the ability to mimic sounds without coaching is largely gone, but may still be present in some people. Many language teachers do not do this kind of coaching, and a few don't even pronounce "erre" correctly themselves.
I'm 35, and I have a friend who's 38. Both of us can't thrill the 'rr'. Everybody notices eventually, has never caused us any problems, never did anything about it. At this point, I don't know if there's anything I can do.
I particularly care about it because I'm learning German and Polish :)
By the way, this is in Buenos Aires, Argentina, where rioplatense-Spanish has (sometimes over-)thrilled 'rr'.
I had problems with that when I was a child, and in high school I had a couple of friends with that problem (I think they never corrected it).
But I think unless you talk a lot with that person you will not notice it in many cases.
This is an old thread but I'm gonna throw in my comment because I have an interest in this subject and have found very little info that is of any real help. I'm from the USA, a native English speaker, and from a family that has been in the US since before it was called the USA (My German ancesters left Germany and arrived in the new world in 1700). I teach English as a foreign language in Colombia. I cannot, even after 8 years of trying, trill the rr. I had a student, he was a doctor and a native Colombian and native Spanish speaker, who also could not trill the Spanish erre. He told me the medical name for the condition but I have long since forgotten the exact name, but I believe it was some kind of "dislalia". It's definitely not common, but it does occur. He told me that in his entire life he never had any problems with communication because of it, and most people don't even notice unless he spent a lot of time talking with them. As much as I would like to trill the erre if it never happens, well, no big deal, I'm communicating with my Spanish friends and others just fine. The only real "problem" I've encountered are the few friends who have tried very strongly to get me to trill the erre, to the point of frustration. Eventually I simply force a change of subject to get past their attempts to help me pronounce Spanish better.