Sounds like you have (at least) two tables, "Project" records, and then the child table which contains these "Expense" records. The budget is dictated on the Parent Table, and each of the Expense records is added as a child to that "project" Am I on the right track so far?
I would create a Summary field on the Parent table that shows the Total $ amount of all of the Expenses (maybe you already have this?). Now on that Parent table you have the Total Budget and the Total expenses on the same record, so we're getting a little closer. Create a formula field to compare the two to see if it is greater or less than 0.
Now that you have that "variance" field, or whatever you'd like to call it, Create a Lookup field of that number to pass that down to the child records. Now each Child has a sense of whether the Parent record is above or below budget.
So maybe you even already have a lot of this. A next step will be to create a formula checkbox that evaluates whether the project is at the budget yet, and checks itself when the project has hit its budget. This field could be hidden from your forms so it can just run in the background.
Now back to your notification. You can set your notification to send when that Checkbox is checked. It will only check itself when the project passes the budget for the first time, so additional expenses don't trigger this notification.
Does this make sense, and does it work? Are there any questions on parts of it that might not be clear or might have missed the mark on?
