Protect string constant against reverse-engineering
We can use "jni module" to keep 'Sensitive Hardcoded Strings' in the app. when we try to reverse engineer APK file we get lib folder and .so files in respective process-folders. which can not decrypt.
You can save your string obfuscated by AES.
In Licensing Verification Library you can find AESObfuscator. In LVL it is used to obfuscate cached license info that is read instead of asking Android Market to find out application is licensed or not. LVL can be downloaded as component of SDK.
I guess you can try a code obfuscator, but really that won't make your password 100% secure and I don't know how well it goes along with the android compiler. Why not use a secured web authentication , like that of Google?