Pronouncing the word "to" with an infinitive in informal American English

Today in class a student asked about the different ways to pronounce the word to prior to an infinitive in informal American English:

• want to see dddx= wanna see
• need to go = needa go
• try to = try da

This came as we were discussing the note on page 265 of the textbook (Grammar in Context 1, Fourth Edition by Sandra N. Elbaum. Boston: Heinle. 2006. ISBN 978-1-4130-0736-7):

In other infinitives, we often pronounce to like “ta” or “da” (after a vowel sound) or “a” (after a “d” sound). [sic] 

That rule seems like a good general guideline, but when to choose either “ta” or “da”? And what about “like to watch”? It does not end in a vowel sound, it ends in a “k” sound  /lɑɪk/ (Source: the Cambridge American English Dictionary via http://onelook.com) and yet the book suggests we use the “ta” sound, and it does sound that way when I say it out loud.

I went to the internet and found some interesting resources. I hope to arrive with more precise instructions by Wednesday. Anyone reading, can you clearly explain when to pronounce “to” as either “ta”, “da” or “a” in informal American English?

Here is one video from ESL Video Courses about infinitives in general,

This video from Rachel’s English is more technical:

I imagine searching through her videos on the letter “t” will help answer:

When do you pronounce “to” as either “ta”, “da” or “a” in informal American English?