Receive 1099 from spouse?

Yes, she can pay you on 1099-misc. You can deduct your actual job related expenses. You will also complete schedule SE. If you have already crossed social security threshold, you will not pay social security tax on 1099-misc income. You will pay only the Medicare tax.
Hope the chief purpose of this arrangement is not to save social security tax.

I suspect the main objective in this arrangement is to be able to deduct expenses for items such as car, computer and phone.

Car: Keep track of mileage for work purposes and deduct at the standard rate/mile. The rate is $0.51/mile for business use from January - June 2011, and $0.555/mile for July - December 2011.

Computer: yes, if the computer is used solely for work purposes (no personal email, internet surfing, gaming, etc). You deduct depreciation of the cost of the PC over its lifetime. If this is a home computer that is not 100% dedicated to work then you may deduct only the cost of software that is required specifically for work purposes. The expense must be for items that are usual, necessary, customary, and reasonable for your business.

Phone expenses: you cannot deduct the cost of a first fixed line into your home, as it is assumed to be used for both personal and business use. You may deduct the cost of long distance calls that are work related, and if you install a 2nd line purely for business you may deduct that as well.

Thanks. The billing and bookkeeping that was outsourced is now handled by me. The expenses related to the travel is the primary reason for the 1099. As her primary work location, my wife cannot deduct the expenses. However, for my travel related to the business, including traveling to her office, I should be able to deduct the expenses. Both answers were helpful.
Thanks

Be careful about travel to the office. That would probably be considered commuting costs if the IRS challenged the mileage.