How can I sing my "E" vowels with more open tone and not cut them off?

I am trying to cover the song "All I Ask of You" from The Phantom of the Opera, and I keep having the same problem on one word. In the line of Christine's that begins "Say you need me..." I am constantly just barely squeaking out the word "need". I want to know if there are any exercises or tips I can use to open up the vowel a little bit more. Thanks!