Since Build Belfiore repeatedly said the preview will be released in the "first part of April". NOT sometime in April. He also said that his comments on that are vague because they don't have a definite date yet. So you can assume that the planned release date is at least a few days BEFORE the end of the "first part of April" (so they have a few days left in case things take longer than planned).
Belfiore's comments are the only official source we have, and from those we can assume, that: The planned release date is at least a few days before April 15th (which technically is the last day of the first "part" of the month), and that any day later than 15th is unlikely.
Since the 12th and 13th are weekend, there are only a few possibilities left: Today, tomorrow, Monday, Tuesday.
Monday and Tuesday seem unlikely for the reasons I explained above. That leaves us with Today or tomorrow.
Besides that, today or tomorrow would make a lot of sense. Today was reported to be the planned release date before they came up with the 14th. According to a leaked mail from MS, bug fixing was planned to be finished by the 8th. And at a Build session, a Cortana engineer said you'll be able to play with the new feature "next week" (which is this week).