My suggestion to you is "DON'T BRING UP THE ISSUE OF H1-B SPONSORSHIP AT THE INITIAL STAGE". By bringing that issue you are scaring most of the recruiters because most of the recruiter think h1-b is a complicated legal procedure and don't want to get involved in it. Just try to get your foot inside the company at the moment. Most of the people I know (including me) got the job because we didn't mention anything about the h1-b sponsorship at the interview. 

Once you get the job and are well acquainted with your manager, you can explain him/her about the H1-b procedure, cost, and other legal requirements.  They cannot fire you citing you provided inadequate information during the interview. This will expose them to the racial or ethnic legal law suit. Once you are in, YOU ARE IN. 

If the company is willing to sponsor, GREAT, good for you. In a worst case scenario, if the company declines to go through the sponsorship procedure, tell them you will hire your own lawyer and bear all the legal expenses, but you will require help from HR in your paperwork. If H1-b legal procedure is completely alien to the company, you would need to explain them about the procedure. Usually, the total cost for H1-b including lawyer's fee range from $4k to $7.5K. This shouldn't be a problem once you get the job. 

For now, don't worry about the H1-b sponsorship, just try to secure a job first. Before you apply for any jobs, think what the recruiter is looking for in the candidate and how you can stand out from the rest of the job candidate. Considering you have had call from over 200 recruiters, I don't think you have any problem with your resume or cover letter. You just need to change your approach and be patient. This is the frustrating stage that everyone has to go through. GOOD LUCK !!! Hope this helps