Maybe, but it will not be easy, from my experience.
On some occasions I have been successful in getting payments from one period applied to another period; but it is not something that the IRS does regularly when you are asking for the estimated payment for this year to be applied to a prior year.
Please understand, even after you get someone that has the authority and ability to make that change that this will be no help at all for eliminating penalty and interest that may be proposed for the prior year. This may help prevent further interest from accruing on the prior year balance due.
The time of the change will be when the IRS records the payment for 2011. There will not be credit for having paid this for 2011 prior to the date that you can get the IRS to make the actual change from the current to the prior tax period.
Making the change may also mean that the current year will not have enough payment after the move.
So, it will be far faster and easier to just make the payment for 2011 than it will be to try to get the estimated payment applied to the prior year (even though it can be done).
Please ask if you need clarification.