Slow lenses? For blurry backgrounds?

Yes, you can create blurred backgrounds even with slow lenses – an f/1.4 lens is great, but even an f/8 lens can give you blurry backgrounds.

How?

By zooming in (using a long focal length lens) or getting close.

Very close. Look at this shot taken at f/8.0:

Not bad, eh. Taken with my Fuji X100 in macro mode-  very close. So yes, you can do blurred background as long as you get close to your subject, relative to the background. Remember that, next time you are regretting not having an f/1.4 lens and having to do with an f/5.6 lens.