Although she did intend to pursue a singing career, her actual ascent to pop-stardom happened somewhat by chance: a friend posted her music to MySpace, where she developed a grassroots following, and got signed later because of this. In fact, it doesn't seem like she is the kind of person who naturally seeks fame or is even comfortable with it: she says about her experience of failure on American Idol: "I was shy. I was nervous. I didn't look the greatest. I wasn't ready for it yet. I was glad, when I auditioned, that they said no." She also describes the physical difficulties in touring and playing music according to a strenuous schedule, as famous artists usually do. This attention to physical qualities is ever-present in Caillat's thinking, which indicates most likely an Si leading or Si ego type. She also worked as a masseuse earlier in her life, a very Si-heavy occupation, and has visual art interests like photography and painting.
While Caillat is friendly and open emotionally she does not express a very wide range of emotions or seem to be prone to emotional excitement. But she emphasizes her relationships with (and maintains a strong connection to) her immediate family and friends and her local community. In fact, her father produces some of her music — she praises his skills, but with her fame clearly she could have chosen somebody else for the job. Her music also tends very much to the "sappy", "sweet" side rather than the emotionally charged or uplifting, which is typical of folk pop. (I don't advocate using an artist's creative work as a sole method of typing, but depending on how much creative control they have, we can see some strong correlations.)
So, overall SLI is most likely. LSE is worth considering also but it would have to be one of the two. Overall there seems to be much more emphasis on Si than Te, although her use of Fe might indicate greater strength than Fe Vulnerable. Caillat made a song about the use of Photoshop that betrays a very common Se vs. Si conflict that may be described as "naturalism vs. control." One area where this conflict arises is in physical appearance.
"I'm against the ways of the world where people feel like they always need to make things look too perfect."
This is a typical (though not universal) approach of Se ego types, which is easy to see in other pop stars like Taylor Swift (SEE), Justin Bieber (ESI), Sia (LSI), Rihanna (LSI or ESI). Si ego types overall prefer a natural, earthy, sensual appearance, while Se ego types tend more towards the constructed, impactful, glamorous, or sexualized. The media turned this message into a soundbite: "Colbie Caillat hates Photoshop" (and then, upon attempts to clarify the nuances of the message, another soundbite: "singer Colbie Caillat actually likes Photoshop!"). More generally, Se seeks to take control of things and make them the way you want them to be, while Si seeks to allow things be the way they naturally are. Se types are also more naturally accepting of the fact that you need to "play the game" and compete for whatever territory is there, even if the way of getting there seems less than savory.
She says she doesn't come up with ideas for songs "in the grocery store" for example, but has to be at home on her guitar, suggesting weaker Ne and stronger Si.
Lots of Si themes both in her music and lyrics, as well as Fi.
[when asked for advice for new artists] "Learn your craft, whatever it is."
"I'm super mellow"
"Music's supposed to make you feel good and smile"
"Family comes first."