It depends what your comfort level is, how stable your job is, as well as what your debt obligations are, as well as your preferred "asset allocation."
To me, how many months of income isn't the point - it's how many months of expenses I can cover. My comfort level changes over time. My cash cushion isn't just (or necessarily even at all) intended for an emergency -- an "emergency" in my life would be a job loss, and I'd probably consider using it as an opportunity to pulls some money out of tax-sheltered savings while my tax rate was low rather than use cash savings first, but that's just because of my particular situation. Instead, my cash cushion is to fund shorter-term things (like 1-2 years out) and my goal with any investment I make is to keep it invested...forever.