I don’t know the answer to your specific question, but if you have access to a computer maybe you could skype if nothing else works.

Voice
$0.02/minute from the US to Singapore. The caller uses Google voice, the receiver can be any phone.

From the Google Voice phone system: Access the Google Voice phone system by either calling your Google number, or if you’re using Google Voice with a non-Google number, calling your access number from a mobile phone registered on your account. Once you’re in the Google Voice system, press 2 to make a call. When dialing an international number, enter 011, the country code, and then the number (for example: 011442012345612345).
http://www.google.com/support/voice/bin/answer.py?hl=en&answer=141922

Saving Google Voice outgoing numbers to your phone’s address book
1)
Set your Google Voice account to forward texts to your cell phone.
2)
Have your friend send a text message to your Google Voice number
3)
The text will appear to come from a 406 area code
4)
Calling/texting that 406 number from one of your Google-voice enabled phones will call your friend’s cell.

I hope that’s clear. If not, ask more questions. It’s very different from normal cell phone usage.

@jaytkay – Thanks! Do you know if Google Voice also allows calls to be made from Singapore to the US, or only US to Singapore?

@xxii I’ve only called within the US and Canada.

Maybe if you both had US phones? (I’m just guessing).

This is unpromising:
“Google Voice text messaging doesn’t support sending and receiving text messages from international numbers at this time. ”
http://www.google.com/support/voice/bin/answer.py?hl=en&answer=117527

@jaytkay I have a new problem. I set up my Google Voice account with my US number as my registered phone, and now I want to add my Singapore number to my Google Voice account so I can use my Singapore phone as a Google-Voice enabled phone. However, it says I can’t add an international number as a forwarding phone.

Is there any way I can somehow switch it or redo it so I can use my Singapore number as my registered phone? Or any other way around this?

Poking around the (rather disorganized) Google Voice help site, I am pretty sure you can only receive GV calls to a US number.

That can be your own phone, or you can get a Google voice number.

So I think GV will only be cheap in one direction – for your friends in the US calling you in Singapore.

Check out net2phone, a virtual international calling card. You can use the access number from any phone and call any number. My family uses it for calling to/from the U.S. and Israel and it’s great and has been very cheap for us.