Solución:
Una opción es usar esto:
UPDATE `calldata`
SET `date` = DATE_SUB(`date`, INTERVAL 7 DAY)
WHERE DATE(`date`) = '2014-01-08'
Violín: http://sqlfiddle.com/#!2/28d71/1
Para un mejor rendimiento, use la siguiente consulta porque MySQL puede usar el índice (si lo hay) como DATE() no está en el lado izquierdo del operador de comparación:
UPDATE `calldata`
SET `date` = DATE_SUB(`date`, INTERVAL 7 DAY)
WHERE `date` >= '2014-01-08'
AND `date` < '2014-01-09
Violín: http://sqlfiddle.com/#!2/7e7b2/1
Prueba esto:
UPDATE calldata
SET date = CONCAT('2014-01-01 ', TIME(date))
WHERE DATE(date) = '2014-01-08'
Comprobar el DEMOSTRACIÓN DE SQL FIDDLE
PRODUCCIÓN
| ID | DATE | DURATION | STATUS | DUPLICATION |
|----|--------------------------------|--------------------------------|------------|-------------|
| 1 | January, 01 2014 19:30:12+0000 | January, 01 1970 00:00:03+0000 | Aborted | (null) |
| 2 | January, 01 2014 19:30:12+0000 | January, 01 1970 00:00:06+0000 | Dropped | (null) |
| 3 | January, 01 2014 05:25:11+0000 | January, 01 1970 00:00:20+0000 | Connected | Multiple |
| 4 | January, 01 2014 05:19:21+0000 | January, 01 1970 00:00:21+0000 | Connected | Repeat |
| 5 | January, 01 2014 05:12:56+0000 | January, 01 1970 00:00:20+0000 | Connected | Unique |
| 6 | January, 01 2014 04:46:56+0000 | January, 01 1970 00:00:41+0000 | Unanswered | Multiple |
| 7 | January, 01 2014 04:42:56+0000 | January, 01 1970 00:00:35+0000 | Unanswered | Repeat |
| 8 | January, 01 2014 04:34:56+0000 | January, 01 1970 00:00:31+0000 | Unanswered | Unique |
| 9 | January, 09 2014 12:06:32+0000 | January, 01 1970 00:00:06+0000 | Dropped | (null) |
| 10 | January, 09 2014 12:06:32+0000 | January, 01 1970 00:00:03+0000 | Aborted | (null) |
| 11 | January, 09 2014 05:25:11+0000 | January, 01 1970 00:00:20+0000 | Connected | Multiple |
| 12 | January, 09 2014 05:19:21+0000 | January, 01 1970 00:00:21+0000 | Connected | Repeat |
| 13 | January, 09 2014 05:12:56+0000 | January, 01 1970 00:00:20+0000 | Connected | Unique |
| 14 | January, 09 2014 04:46:56+0000 | January, 01 1970 00:00:41+0000 | Unanswered | Multiple |
| 15 | January, 09 2014 04:42:56+0000 | January, 01 1970 00:00:35+0000 | Unanswered | Repeat |
| 16 | January, 09 2014 04:34:56+0000 | January, 01 1970 00:00:31+0000 | Unanswered | Unique |
| 17 | January, 09 2014 12:19:01+0000 | January, 01 1970 00:00:20+0000 | Aborted | (null) |
| 18 | January, 09 2014 12:19:01+0000 | January, 01 1970 00:00:19+0000 | Connected | Repeat |
| 19 | January, 09 2014 12:15:30+0000 | January, 01 1970 00:00:20+0000 | Aborted | (null) |
| 20 | January, 09 2014 12:15:30+0000 | January, 01 1970 00:00:19+0000 | Connected | Unique |
| 21 | January, 09 2014 07:25:11+0000 | January, 01 1970 00:00:41+0000 | Connected | Multiple |
| 22 | January, 09 2014 07:19:21+0000 | January, 01 1970 00:00:27+0000 | Connected | Repeat |
| 23 | January, 09 2014 07:12:56+0000 | January, 01 1970 00:00:20+0000 | Connected | Unique |
| 24 | January, 09 2014 06:46:56+0000 | January, 01 1970 00:00:32+0000 | Unanswered | Unique |
| 25 | January, 09 2014 06:42:56+0000 | January, 01 1970 00:00:29+0000 | Aborted | (null) |
| 26 | January, 09 2014 06:34:56+0000 | January, 01 1970 00:00:27+0000 | Aborted | (null) |
| 27 | January, 09 2014 05:34:56+0000 | January, 01 1970 00:00:27+0000 | Aborted | (null) |
| 28 | January, 09 2014 05:25:11+0000 | January, 01 1970 00:00:41+0000 | Connected | Multiple |
| 29 | January, 09 2014 05:19:21+0000 | January, 01 1970 00:00:27+0000 | Connected | Repeat |
| 30 | January, 09 2014 05:12:56+0000 | January, 01 1970 00:00:20+0000 | Connected | Unique |
UPDATE calldata
SET date="2014-01-01"
WHERE DATE(date) = '2014-01-08'
Demostración de SQLFiddle
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