User6726 is absolutely correct, but to expand a little bit:
The "more to follow" idea comes from Gricean implicature, not from the words themselves.
Grice's Maxims are four rules that people "expect" everyone in a conversation to follow. One is the maxim of relevance: if you're saying something, you're saying it for a reason, so it should be relevant to the context. Another is the maxim of quantity: you'll say as much as you need to get the point across.
"I have an idea" on its own generally seems to violate either relevance or quantity: in most contexts, that doesn't really add anything or give any useful information (bad relevance), and if the idea is relevant, you haven't said enough about it (bad quantity). But if you followed it up with "…we could foo the bar", that would fulfill both relevance and quantity. So people will be expecting that followup—it's the only way the first part makes pragmatic sense.