You should pass. For one, you already have consumer debt on your CCs (though you'd get a bit of a pass if your CC debt was from medical bills or something else non-consumery). You need to totally get out of that and into living within your means before taking on more consumer debt. And frankly, I would pass then, too. Instead, just save up the money beforehand.
Also, Havertys is wayyyy overpriced IMO and you are basing this off of a min. of $3k. Do you really need $3k worth of furniture or is the "deal" encouraging you spend more than you would? Honestly, the fine print of the store when we bought our furniture was that "cash" (just not financing with them- we paid with a CC that we pay off every month) got us 10% off. Suddenly 0% wasn't so free.
If you miss one payment you'll get socked with late fees and a higher interest rate. For $3k, an amount that is attainable with a few months of saving, I'd just wait until you can pay for it outright and leave the CC lifestyle totally behind you.