Unquestionably, in temple times, there is a positive commandment for cohanim to bless the people on a daily basis. This was performed after the offering up of the incense. However, it is important to decipher the extent of the obligation today, in times when the temple is yet to be rebuilt.
The Sde Chemed brings an amalgamation of later authorities including the Pri Megaddim and the Mabit that consider the obligation to remain on a scriptural level even today.
The next step is to investigate quantitatively their requirement to bless. The Rambam and the Chinnuch comment that the obligation is to bless the Jewish people on a daily basis. Fascinatingly, the Minchat Chinnuch (Mitzvah 378) claims that a cohen that blesses more than once in a day, performs a positive commandment every time he blesses. He considers the Mitzvah similar to that of Tefillin in that a person is required to wear them daily and one transgresses this requirement by failing to wear them at least once in that day. However, should a person put on his Tefillin for a second time during daylight hours; he would fulfill the commandment a second time. So too with the priestly blessing. The cohen performs a mitzvah every time he blesses.
The Beit Yosef (Ohr Hachayim 128) is left with the perplexing question: If the cohen performs a scripturally based commandment by blessing the Jewish people, then why are they lax in their duties? He quotes the Agur who claims that since their custom is to immerse themselves in a mikvah before recitation of the blessing and this would be too difficult to perform during winter months, as a result they made an overwhelming decision not to obligate themselves in this mitzvah. (The cohen is not obligated if the community does not call him to bless.) The Beit Yosef himself does not agree with this reasoning as there is no Talmudic support that obligates the cohen to immerse before the recitation.
The Kaf Hachaim (128,271) feels that it makes more sense for them to bless on a daily basis and indeed the custom in the landof Israelis to follow this view.
The great Ashkenazi posek, the Rema, maintains the custom not to bless and suggests a rational: since people are overburdened with financial constraints and worries, the cohanim are not in a state of the necessary happiness that is needed to be able to bless the Jewish people with love. A notable exception to this rule is Yom Tov where the scripturally ordained rejoicing prevails and hence the cohen is able to bless.The Aruch Hashulchan makes an interesting point; there is no justification for the cohanim not to make the priestly blessing. However, historically, rabbinic leaders have failed in their attempts to re-establish the custom for them to bless and it is as if a heavenly voice is restricting our ability to resurrect this scriptural commandment in our exile. This is in line with the above statement of the Rema and the opinion of the Zohar.