D.B. Weiss, George R.R. Martin and David Benioff, with castmembers Rose Leslie and Emilia Clarke.
We now have one firm answer. Benioff and Weiss have confirmed that, although their #1 preference is for the books to come out first, they will not put the show on hiatus for a year or two as some fans have suggested. They do not want to lose momentum or have to recast the younger actors.
They're as worried about when the remaining books come out as you are: Actually, "I guess we spend more time worrying than the fans," Benioff said. The two of them visited Martin at his home in Santa Fe back in February to pump him for information about where all the stories are going, so they can properly set them up in the world of the show, and "It was incredibly useful," according to Benioff.Finally! The claims that the multi-million dollar show could go on hiatus for years on end whilst they patiently wait for the final two books were always extremely unrealistic, and it's good to have that officially spelled out at last. Note that this does not mean that they will catch up with Martin - they still have several years' grace and Martin is some way into the next book - but they are prepared for the possibility.
"There's no question that this will be better for us if the books come out before the various seasons come out," Benioff added. "That said, we're not going to take a two-year hiatus (to wait for a book). The little kids are growing older, the show's got momentum now, and the show must go on. We're just hopeful that it will all time out."
In addition, Benioff and Weiss have reiterated that, whilst they know the audience wants 12 episodes a year or more, they cannot physically make any more. I've always been doubtful about that claim. Whilst GoT's production schedule is hectic, it's nowhere near as hectic as others. Doctor Who shoots 14 episodes a year by filming over nine months (as compared to GoT shooting 10 over six), so GoT can definitely step it up. They'd need to delegate more scripts to other writers and HBO would need to invest more money, but given the show's overwhelming popularity this should not be insurmountable.
In another interview (the link eludes me for the moment) Benioff and Weiss also said that the show was approaching its halfway point, seemingly confirming speculation that the show is going to last for 7 or 8 seasons.