I don't seem to be able to find the ATTiny's current consumption anywhere (at least not in a form I can recognise!), but the max load from the led is going to be 20mA.
It varies a lot with things like clock speed, what parts of the chip are enabled and the amount of slumber you use. With the right programming it can be down in the nanoamps range...
See the section "Power management and sleep modes" in the datasheet. You should definitely switch off the Analog circuitry, that's a big power hog. Switch off anything else you're not using, too, like USI and timers.
Just by running at 1mHz and switching off the unused parts of the chip power consumption will be a lot less than your LED, maybe a milliamp or two. By sleeping in between LED updates you could get it down to microamps.
Here's an article on AVR power optimization: http://www.gammon.com.au/forum/?id=11497
It's not a Tiny85 but the same principles apply.