This answer is based on common workplace practices in the Indian IT industry. (I assume asker is from India, based on his display name, Venky.)
In the Indian IT industry, notice period ranges anywhere from 1 month to 3 months, and it is somewhat painful to note that companies are increasingly moving towards the upper end. However, that doesn't necessarily mean your life has to be full of despair. Attrition rate in India still remains very high despite the lengthening notice periods.
Your notice period during probation is typically half of the "normal" notice period. An employee is typically placed on probation for 3 months to 12 months. However, this is usually just written in the offer/appointment letter and the end of probation is not celebrated with much song and dance. You haven't mentioned how long you have been with the company. Read your offer letter carefully, you might still be on probation without realising it!
Many companies also have a so-called "notice period buyout" option in their hiring policy. This means, for example, you can reduce your notice period by paying the equivalent "basic salary". Since companies hire people from other companies all the time, a lot of them make it easier for the candidate by offering to reimburse this notice period buyout money.
Don't expect your current manager or HR to helpfully remind you of this policy or suggest you to use it. :) Read the company policy yourself. Be aware that the "basic salary" is not your full salary, but only one component of it. Also note that to seek reimbursement from your new employer, you need a written statement from your current employer mentioning the amount of notice period buyout paid by you. If you quit the company without this document in hand, you can pretty much forget about the reimbursement.
You should avoid asking about the notice period buyout to your prospective employer in the initial rounds of interview. Discuss this only with the HR, and wait until they bring up the topic of notice period. If you know some other employees in the company on a personal level, you can also try to get this information from them, without jeopardizing your interview.
Next option is to just make a harder and more focussed search. As mentioned above, the 3 month notice period is now becoming increasingly common. Other companies also know this, so companies which accept the 3 month notice period are not so rare to find. In my experience, the "product based" companies typically offer a greater leeway in the joining dates, as against the "service based" companies, so you might consider focussing your job search on such companies.
If you plan to attend interviews during your notice period, you will have to do a very hard balancing act. Since you say your current workload seems unbearable, it might not be easy, but it is not impossible. You will have to stretch yourself a lot if you choose this option. You may find it difficult to get leaves during the notice period.
If you work more or less independently, you could offer to work on weekends in return for leaves on weekdays, during which you could attend interviews. If you have already resigned, and unless your manager is a complete jerk, he/she would understand that you need to attend interviews to get another job.
- If you do plan to serve out your notice period and then look for jobs, be prepared with a good answer for the question, "why did you leave your last job without another offer in hand?". Despite how you feel about the situation, don't say anything which would reflect on you negatively, such as, "I couldn't bear with the workload", "I hated that place", "My manager was an idiot", etc. "I needed to take a break to take care of some important personal matters" usually works well enough (I have tried it myself when I was out of job for a while, but for a different reason), but what you say is really up to you to decide.