Not an SAHM perspective, but when my DD was 3, the answer was, "Pretty much whenever I was home and she was awake." Or, if you prefer, "Enough to draw complaints from DW from time to time," since my perceived obligation to entertain DD sometimes meant other things I needed to get done weren't. Working all day and then immediately going into a childcare role for the rest of the evening and weekend can be pretty stressful.

It was about this age that I started recognizing that I needed to put in certain limits, because my patience has one, and exceeding my patience on a daily basis wasn't going to be good for either one of us. So...

- No dolls.
- I would make allowances for other activities she wanted to do that I was less enthusiastic for, but only for a certain amount of time, and we'd have to go do something else. Kids at that age like to switch up activities anyway, so no worries.
- I introduced her to things I enjoyed doing, to see what would stick. The more things we both enjoyed, the more profitable for both of us any play time would be.

The benefits of imaginative, free play cannot be overstated. Here's the simplified version:
http://www.livescience.com/15541-top-5-benefits-play.html
And the long version:
http://www2.aap.org/pressroom/playFINAL.pdf

In your situation, my reasonable boundary would be, "Not until I've had my morning coffee." Feel free to substitute whatever morning ritual works for you.

And remember... she'll only be 3 once, and it'll be over before you know it.