I agree agree with LP in the case of low funds. What if the OC does not approve the funding later and you are out of pocket?
The OC really should bite the bullet and have an adequate sinking fund plan, including a levy each year to fund the plan, and the plan should have a substantial contingency component. Plan for both the known expenses and the likelihood of some unknown expenses. Build up a comfortable buffer and it will be no big deal if some expense is required earlier than anticipated in the plan or something else turns out to be more expensive than anticipated.
Unless your tree presents an immediate, urgent, serious threat that demands immediate action, I would suggest that you just call the meeting with proper notice and get the levy approved and get on with the tree after perhaps only a month or so of delay. Putting hazard cones around or roping off the area would underline the importance of getting the approval.