Hard to say for sure without the scene file but my guess is that your spline doesn't have enough points to project properly. Make the text editable if it isn't already and then go into points mode to see what it looks like. Keep in mind that the projection command won't create any additional points, so if there aren't many there you'll need to use the subdivide command or the knife tool to create more.
I converted it to an editable spline, otherwise it wouldn't allow the use of the project tool.
I copied both elements into a new project and still wouldn't work, so I created a new cylinder, made it editable and deformed it to match the curvature of the original object. Then I hid the original and projected the spline onto the new cylinder; then worked correctly. I used xy plane projection. After that I deleted the cylinder and unhid my original shape.
I'm still not sure what was wrong with the first object, but the problem laid with that, not the spline, maybe because it was triangulated? Very weird.