It would be nice if the JSON you posted was in the correct format! Also, there's an extra ":" in your date format string.
Treating the data as a plain text file, this will work:
$x = Get-Content C:\junk\j.json -Raw
$today='{0:yyyy-MM-dd}' -f (get-date)
$y = $x -creplace '"target": "\d\d\d\d-\d\d-\d\d"', """target"": ""$today"""