Checkbox If Today
First, if you just want to checkbox if today, here is the formula:
formatDate(prop("Date"), "MMM DD, YYYY") == formatDate(now(), "MMM DD, YYYY")
Checkbox Today and Remain Checked
dateBetween(prop("Date"), now(), "days") <= -1 or formatDate(prop("Date"), "MMM DD, YYYY") == formatDate(now(), "MMM DD, YYYY")
Breakdown
(dateBetween(prop("Date"), now(), "days") <= -1
If days between a date property and today is less than or equal to -1 …
or formatDate(prop("Date"), "MMM DD, YYYY") == formatDate(now(), "MMM DD, YYYY"))
or if date is today …