You should expect your stamp about six months from the time the application is received by the BATF. After they get your application it may take 2-3 weeks for them to cash your check and they don't begin the review process until the check clears. Once the review process is complete, if they approve the application and issue the stamp, it may take about a week for you to receive the approved application in the mail.
Anyway, if the ATF cashed your check in early January, you SHOULD get your stamp sometime around the end of June- early July time frame. OTOH, if you get a letter saying there was an error of some sort with your application, add about two weeks to that along with the time it takes to correct the error. BTW, if you get a letter saying you need to correct something and don't return the form & error letter within 30 days, ATF will cancel the application and you have to start again.
"... Americans... we want a safe home, to keep the money we make and shoot bad guys." -- Denny Crane