EDIT: I am still contributing to my 401k of course regardless of what I do with my take-home pay.
Personally, I am a fan of dumping the balance of the EF, up to the legal max, into a Roth before each year's annual deadline (so before 4/15 of 2013 to make the contribution for 2012, put in $5K or $6K depending on your age, unless you are married, in which case double those amounts counting a spouse's account, to which you can also contribute -- this would, of course, assume combined finances), and keeping it in cash or cash equivalents if it's doubling as your EF (which in this model you would be). You can then withdraw that contribution anytime you need to (i.e. if you have an E).
Of course, this is only worth doing if you can distinguish between a true E and a faux E, and if you can't contribute to both a Roth
and an E-fund. But I for one, finding myself so situated (able to distinguish between the 2 types of Es but unable (or insufficiently committed as the case may be) to fund both accounts) have been doing this for years. Obviously you don't need to keep more $$$ in the Roth in cash equivalents than you would want to have on hand in an EF.