Is charity obligatory merely by uttering "I will donate" with the intention of donating specific money, or is the phrase incomplete and not considered an obligation?

Nothing is binding upon you, for what you uttered is not considered meaningful speech that entails any consequence. Even if you had uttered a complete sentence, such as a promise to donate, it would not be binding. So, cast aside these whispers (waswas) and occupy your thoughts and time with what benefits you in this world and the Hereafter.