Thank you for your question. To give our specialist a little more information to aid in identifying the culprit, could you tell me where you live?

Omaha, NE

It is probably a tobacco budworm caterpillar; could also be a hornworm as you suggest.

Hornworm larvae have a thin 'horn' projecting at their tail end; budworm caterpillars do not.

For control a low-toxic approach would be to use a spray containing Bt (Bacillus thuringiensis), or an insecticidal soap starting at flowering.  Moths are attracted to lay eggs on flowering plants, and it may be at risk from infestation as long as it is flowering; so repeated applications may be necessary.