Glad to help…
So a few things…
Firstly, don't go out and buy another hard drive. I will recommend a few things here for you.
By the way, this is a very good article, http://support.apple.com/kb/HT1427Time machine 101 - there is a section on "Backup drive fills up"
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1st option - create more room on the time machine drive.
What you can do is navigate your current time machine hard drive just like any other drive.
-You will find a folder titled backups.backupdb/the name of your mac/ and then a bunch of folders that have numbers.
The / (foward slashes represent a jump from one director or folder, to another)
You will eventually find a list of folders that look something like the list below:
2012-06-21-201345
2012-06-22-005847
2012-06-24-202225
2012-06-25-002744
2012-06-26-001425
2012-06-27-001427
2012-06-28-001428
2012-06-28-171503
2012-06-29-102107
2012-06-29-111403
2012-06-29-120354
2012-06-29-130406
2012-06-29-140354
2012-06-29-153323
2012-06-29-163212
The folder names follow this sequence, yyyy-mm-dd-hhmmss
Those are my backups for example.
-So, with that said, you could manually delete the oldest backup. If the list above were your mac, I would be moving to the trash the 2012-06-29-163212 folder.
2nd option - consider this but I doubt it will help but try before deleting data.
If we consider the following from the Apple support article:
As your backup drive begins to fill up to its capacity, Time Machine intelligently deletes the oldest backups to make room for newer ones (and will alert you if the "Notify after old backups are deleted" option is selected in Time Machine preferences).
Then the steps below may help because you should not be necessarily getting a hard drive full warning although you may. So if I would delete anything it would be my oldest backup folder.
Maybe we should simply try to link the backup drive to the time machine preferences, I doubt this will solve it though. Allow time machine to complete the preparing stage and begin a backup. If you interupt time machine backups they don't cause harm but they will cause the next backup to take longer than expected as it has to audit things.
To do this;
-open time machine system preferences
-click select disk
-click 'do not backup'
-click 'select disk'again
-click your target backp drive in the list
-click 'use back up disk'
The backups wil continue not start over, don't worry
As an addendum, re-building the spotlight index is also helpful but again, I doubt it will mitigate any change and it can take hours but it will complete.
Time Machine backups rely on a clean spotlight index so
To do this;
-open spotlight system preferences
-click the privacy tab
-drag and drop your boot drive into the list under the privacy tab
-close the system preferences
-your spotlight index will be gone, to test this, try a spotlight search nothing will come back
-now, open spotlight system preferences
-click the privacy tab
-remove the hard drive you dragged and dropped into the list and close system preferences
-if you click spotlight form the upper right corner you will notice it is indexing, backups can not take place while this happens.
Final words
Let's try these things before considering a new drive.
-please, if something is not clear, write back