There's a company called Marketing Experiments that has done quite a bit of research into how you can manipulate a landing page to control the rate of conversion. I don't know how much of their content is available online (their conferences are not cheap - but they're very high quality), but you can get a feel for it at their website: http://www.meclabs.com/training/workshops/lpo/overview
While I realize that this won't provide you with an authoritative answer, perhaps it'll help (or at least point you in the right direction).
The summary of what they discussed is that the primary factors affecting the conversion rate are (in order of greatest to least):
- The motivation of the user to buy the product
- The clarity of the value proposition (ie, statement of the value they will receive by providing you with their email/name/credit card/etc)
- The friction (ie, number of form fields) of the page, which is primarily offset by the incentives offered to continue (ie, free stuff)
- Negatively, the anxiety of the user
So, while the number of fields on the form does play a pretty important role in affecting the rate of a conversion, it's not the only factor. If you do find that you need to have a lot of form fields, you can balance the "friction" by adding more incentive for the user to continue.
However, they did also mention a very interesting technique to help address the problem where too much friction reduces conversion quantity, whereas too little reduces the quality:
- Split the form into two pages. On the first page, collect a small amount of information (name, phone number, email address).
- On the second page, ask the user for the additional information you're looking for (answers to questions, physical location, etc)
Be sure to save the information collected from both pages in your database. That way, you have a list of quality leads (the people who completed both pages), but you also still get the high quantity leads (ie, the people who just completed the first page).
So, if your client is insisting on a large number of form fields, my recommendation would definitely be to split the form and move some of those questions to a later page in the process.
Also, my second suggestion to you would be to run tests on the form and see which one works better (ie, show the shorter version to half of your visitors and the long version to others and measure the conversion rates). There are some pretty nice tools available (Google's Website Optimizer is one) that'll allow you to do these types of experiments to conclusively determine what configuration of a page will result in the optimum rate of conversion (in terms of both quality and quantity).
(By the way, I would highly recommend the training course I mentioned above; they've invested a LOT of time into the marketing research process and the information they share with you is incredibly valuable).