UPDATED | December 7, 2018:
According to the December 7 Ethereum core devs meeting, Constantinople is set to be implemented at block number 7,080,000. It is still estimated that this will occur around January 16, 2019.
ORIGINAL | November 9, 2018:
During the latest Ethereum core devs meeting, held today, the developers set Wednesday, January 16, as the date to implement the upcoming Constantinople hard fork on the mainnet. This date is subject to change if issues arise or other considerations are brought forward between now and then.
The upgrade was originally slated to hit the mainnet around Devcon4 (which took place from late October to early November), but there were a variety of issues that contributed to its delay. Some of these were a consensus snafu with the Geth and Parity clients over the Ropsten testnet, a lack of communication between clients and miners (there were no miners who had implemented Constantinople on Ropsten), the apparent absence of a hard fork-specific forum for Ethereum, and the time developers spent at Devcon4.
Although Constantinople could be further postponed, core dev Lane Rettig noted that due to the difficulty bomb, block times would start to appreciably increase around early to mid-January of 2019, with the 30-second threshold being reached by early to mid-May, perhaps as early as April. He explained that even though with the previous hard fork, Byzantium, there was a longer period (seven to eight months) during which block times could increase, the total difficulty on the network is much higher now, meaning block times would reach 30 seconds in a shorter period.
Toward the beginning of the Constantinople discussion, core dev Holger Drewes suggested an alternate hard fork schedule: December 10 for the start of a new proof-of-work testnet (thus making Ropsten obsolete), January 16 to implement the upgrade on this new testnet, and then February 12 as the date to activate Constantinople on the mainnet. However, he ultimately decided to drop his suggestion in favor of the mid-January date.
Core dev Afri Schoedon added over Twitter that the final block number for the upgrade would be confirmed on Black Friday (November 23).