The Core

It depends but if the site is relatively poorly ranked I used to say at least double. Double turns them on.

Agree with nffc - if they have had some good work done, turn them down. If not, you should be able to double it easy.

The harder question is "How long?" 

"How much of a jump in traffic should I expect from your efforts?"

I generally respond with a more polite version of

'you are asking the wrong question .... you should be asking 'how much profit will you make me?', and the answer to that largely depends on how much you follow my advice. Traffic without 'conversions' is a 'cost' blah blah blah "

........  then I would pitch for a 'conversion improvement' contract as well.

I don't really like doing client work unless I can also do some conversion improvement work as well - if they aren't making enough profit from what I do, they won't carry on paying me for very long.. and for most of our clients, conversion improvement is an easier way to make a difference that matters to them.

... of course, depends on loads of factors as per other comments.