Your accountant is giving you reasonable numbers. At $95K net, the S-corp election typically makes sense, but the math depends on what you set as a “reasonable salary.” The IRS requires S-corp owner-employees to pay themselves a reasonable salary before taking distributions. Only the salary portion is subject to FICA (Social Security and Medicare) tax.
For a consultant netting $95K, a reasonable salary might be in the $55K–$65K range depending on your industry and geography. The remaining $30K–$40K would come as a distribution not subject to the 15.3% SE tax. That is where the $4K–$5K savings comes from.
The break-even point where S-corp typically makes sense is around $50K–$60K in net self-employment income after deductions. Below that, the additional compliance costs (payroll service, separate tax return, potential state-level S-corp taxes) tend to eat up the savings. At $95K you are solidly above that threshold.
Regarding Form 2553: the deadline is 75 days from the start of the tax year, which for calendar-year entities means March 15. If you miss it, you can file a late election with reasonable cause, but do not count on that. Make a decision before March 15.