I was wondering whether it is possible to visit the US on a tourist visa while I am waiting for my alien resident visa, which I will have within the next few months?

good luck trying! Chances are close to 0.

Can't you go on a visa waiver? I did.

I was advised against it by by immigration council and by the US embassy.

Basically its not what the visa waiver program exists for. You may be okay, but if questioned your Application may be jepordised. In my mind the risk would not be worth it...

D

I did it every month for 2 years. I was advised by a lawyer that I was to carry proof that I was returning to the UK, like mortgage statement, bills, letter from my boss etc. I can't say I advise it, as it is a risk, but I did do it. I actually scaled down my visits in the end because I did worry about it.

I was advised against doing it at the American embassy in London, so I didn't risk it because I didn't want to hinder my residence visa process.
In the end I flew to Canada and my fiancee met me there - luckily she was near the border so could drive up and I have relaitves in Canada who were willing to put us up for a few weeks.

I did it once, came in for 2 weeks but stayed for 88 days.

They are not so much interested why you want to come in, more that you will be leaving, job etc. If you can show that you will be leaving you should be OK.

But when it all comes down to it nobody can guarantee it. It is all down to the the Immigration officer.

visajourney.com is a good board if you have not come across it so far.