I've always been a little wary about using a HELOC as one's only emergency fund. It's a nice theory, but in a real emergency - job goes away, perhaps home equity is whacked, credit deteriorates, etc - there was never any guarantee that the bank wouldn't freeze the line and no further withdrawals against it just when they are needed - not much of a safety net.
Turns out that some folks HELOCs *are* getting frozen:
[and there's a link to an LA Times story dated Feb 1 a little way down that page, which is an interesting story, too]
which I found from:
The bottom line seems to me to be that even if you are earning less on a savings account than you are paying on a HELOC, don't use all your savings to pay that thing off. Do work on paying it down, but that interest difference, which may be as much as 3 or 4 percent per year (assuming a high-interest savings like ETrade or HSBC and a HELOC somewhere around prime) - is the cost of *guaranteed* liquidity - exactly what one needs in an emergency fund.
And if there are folks out there with no cash emergency fund but an open and available HELOC - they might be advised to actually extract enough cash from that HELOC - now - and park it in cash while they know for sure they can.
[Oh, and credit cards are probably an even worse "emergency fund" plan...]