It's actually the opposite mistake, as Tolkien notes in "The Battles of the Fords of Isen" (published in Unfinished Tales, my emphasis):
When Théodred was at last slain Saruman's commander (no doubt under orders) seemed satisfied for the time being, and Saruman made the mistake, fatal as it proved, of not immediately throwing in more forces and proceeding at once to a massive invasion of Westfold.
Tolkien then goes on to note what would have happened if Saruman had acted earlier:
If the invasion of Westfold had begun five days earlier, there can be little doubt that the reinforcements from Edoras would never have come near Helm's Deep, but would have been surrounded and overwhelmed in the open plain; if indeed Edoras had not itself been attacked and captured before the arrival of Gandalf.
In an author's note to this essay Tolkien then goes on to discuss the Ents:
The Ents are here left out of account, as they were by all save Gandalf. But unless Gandalf could have brought about the rising of the Ents several days earlier (as from the narrative was plainly not possible), it would not have saved Rohan. The Ents might have destroyed Isengard, and even captured Saruman (if after victory he had not himself followed his army). The Ents and Huorns, with the aid of such Riders of the East-mark as had not yet been engaged, might have destroyed the forces of Saruman in Rohan, but the Mark would have been in ruins, and leaderless. Even if the Red Arrow had found any one with authority to receive it, the call from Gondor would not have been heeded – or at most a few companies of weary men would have reached Minas Tirith, too late except to perish with it.
The First Battle of the Fords of Isen was on 25th February, according to the "Tale of Years" (Lord of the Rings, Appendix B) and this was the battle in which Théodred was killed, and therefore obviously the one referred to in the first quote above.
The Second Battle of the Fords of Isen was on 2nd March ("Tale of Years"), or 7 days later (February in the Lord of the Rings calendar for that year had 30 days), in which Erkenbrand was defeated. Saruman's main invasion of Rohan must have begun on or before that day, because the "Tale of Years" also notes that the Ents reached Isengard on the night of the 2nd.
The Battle of Helm's Deep began on the 3rd of March, the same day as the Ents completed the destruction of Isengard.
Going by these dates, the "five days earlier" that Tolkien refers to above must have been the 26th or 27th of February; notable dates for comparison with other events are (all from the "Tale of Years"):
- 26th February: Breaking of the Fellowship, capture of Merry and Pippin.
- 27th February: Éomer pursues the Orcs.
- 28th February: Éomer overtakes the Orcs.
- 29th February: Merry and Pippin escape and meet Treebeard, the Orcs are destroyed.
- 30th February: Entmoot begins, Éomer meets Aragorn.
- 1st March: Entmoot, Aragorn meets Gandalf.
- 2nd March: Healing of Théoden, end of Entmoot, Ents march on Isengard.
An earlier invasion of Rohan would therefore have obviously disrupted all of these events.