If you're a business owner in the United States, most likely you pay estimated tax payments 4 times a year. Here are the days when the payments are due this year:
Tuesday, January 15
Monday, April 15
Monday, June 17 (The usual day when this payment is due is June 15, but that happens to fall on a Saturday this year. In that case, the deadline is extended to the following business day, which is Monday, June 17.)
Monday, September 16 (The usual day when this payment is due is September 15, but that happens to fall on a Sunday this year. In that case, the deadline is extended to the following business day, which is Monday, September 16.)
These dates indicate the day by which the estimated tax payment needs to be mailed (postmarked), so it's okay to mail on the day that it's due (provided you do so in time to get a postmark from that day).
If the day when the payment is due falls on a weekend or an official holiday, then you can mail the payment the following business day, and it will still be counted as being on time.
By the way, that tax payment in January is actually for the last quarter in 2012, in case you were wondering.