I can count over a dozen other women (and one man last year) who "stayed home" with the kids and made it work. The trick is to pare down your monthly expenses as much as possible and stick with fixed expenses (if possible) For example, we live in on-campus housing so we only have one car, zero commuting expenses and electric/phone are part of our rent. I'm still a little shocked that it worked, but we made it through MS1 with little-to-no additional loans or income. This year I am still "home" with the kids, although I work three nights per week, essentially to pay off our car loan and credit card bills. If you have little or no consumer debt, you should be able to make it. However:
Get your child (and hopefully your wife, too) onto a state medical assistance program and sign up for WIC (monthly certificates for free milk, juice, etc..., as well as formula if your wife is/begins bottle-feeding). This may not be possible until you start school and your income drops, but look into the qualifications in your state.
You and/or your wife should consider a part-time job in the evening (if you will be living near the hospital, this is a great place to look) nothing major, just one or two nights per week. You should be able to handle one night per week with your MS1 schedule (especially if you find a job where you can study!), and you will get quality one-on-one time with your child while your wife gets a "break" once or twice per week. This income will be a big help, not to mention you will most likely qualify for the "Earned Income Credit" on your taxes.
You should also get an extended summer break after MS1 when you can work.
Remember that, unless your wife is able to step easily into a $50,000+ job, working can be MORE expensive for you. Day care costs, health insurance costs and your reduced qualfication for financial aid in subsequent years, can make full-time work very uneconomical and more stressful on your marriage. I have two graduate degrees and six years of professional experience as a teacher, but full-time childcare alone would cost us more than $1200.00/month. Add in the cost of employee-sponsored health coverage, commuting expenses, clothes, etc.. and I wouldn't be "making" anything. We simply CAN'T AFFORD FOR ME TO WORK FULL-TIME. Money may be tight, but I'm less stressed than I was as a full-time working mom, and we have ALOT more family time than we did prior to medical school. Scan previous posts on the spouses/partners forum.
Good Luck!