The answer is...maybe :)
Lets take Jupiter as one example to start with:
To be earthlike you need:
- 1 bar of pressure
- temperature around 0->40 degrees centigrade, around 300 degrees K
- an oxygen/nitrogen atmosphere
Looking at Jupiter then you do get 1 bar just above the cloud layer, however the temperature is only 100k at that point. The water cloud level happens lower down, where you do get the required temperature - but you also get ten times earth's atmospheric pressure. At different points in the atmosphere you do get both earth-like pressure and earth-like temperature (although not at the same point).
In theory if the planet had a different composition or orbited at a different distance from the star those two points could be made to line up. Sudarsky's Gas Giant Classification system looks at the various known types of gas giant. Class 2 Gas Giants in particular actually have Water clouds which again is encouraging from the point of view of pressure and temperature.
The problem is composition: Jupiter's atmosphere is composed of about 90% hydrogen and 10 % helium. There are only minute traces of methane, water, ammonia, and rock dust.
So, this is your main problem. The gas giant would need a radically different composition from anything we've ever heard of in order for it to have a high enough percentage of heavier gasses like nitrogen, especially at the altitude where the atmospheric pressure is survivable for humans. You should also consider that Oxygen is highly reactive. If you do not have lifeforms of some sort creating it you are very unlikely to find free oxygen, it will all react away.