Hi Lisa
I would not recommend attempting to estimate an epic. An epic is something that is going to take a considerable amount of effort and is usually made up of several if not dozens of stories and possibly hundreds of tasks.
It sounds like what is being asked for is more like a Rough Order of Magnitude (ROM) estimate which comes with a threshold of -50% to 200% variability in what is quoted which most managers and up find of little use.
I would stay firm with the team on insisting you break down the epic(s) to user stories and if possible tasks. For a rough estimate and depending on the complexity of your epic a one-day workshop (or less) might be all that is necessary to attempt to estimate the entire epic.
Just some ideas and suggestions. Some great strategies are outlined in Estimating and Planning by Cohn and Cyrstal Clear by Cockburn
Hope this helps,
Chris