UPDATE: I wrote this answer in 2015, and it was accepted as the best answer. Since then, new information is available which provides a better answer. I have up voted DavePhD's answer and hope others will as well.
ORIGINAL: At this point, the only accurate answer is that we don't know for sure. This study indicates that Antarctic ice is increasing overall, while many other studies indicate that it is decreasing. This study used data only from 1992 to 2008, while other papers using more recent have reached the opposite conclusion. Even this study indicates that the rate of ice gain is slowing, and will become a net loss in the future.
Robert McSweeny has written a good summary of the recent article, with some comparisons to other studies. The study was done using satellite-based lasers to measure ice thickness over different regions in Antarctica, from 1992 to 2008. The study found that the Antarctic Peninsula and West Antarctic Ice Sheet (WAIS) both lost ice during that time, and the East Arctic Ice Sheet (EAIS) accumulated on average about 1 cm of ice. Overall, the study found that there was a net increase of ice.
The study concludes that the gains in ice over East Antarctica outweigh the losses on WAIS and the peninsula between 1992 and 2008.
According to the study, Antarctica has been gaining ice for about 10,000 years:
So, where is this extra ice on East Antarctica coming from? The researchers say it all started around 10,000 years ago, at the end of the last Ice Age. As the air warmed up, it could hold more moisture, and the amount of snow that fell onto the ice sheet doubled. Since then, this extra snow has gradually been compacting into ice, making the ice sheet thicker.
But the study also measured a reduction the overall Antarctic ice gain, i.e. ice losses in other parts of Antarctica are catching up with ice gains in the EAIS:
But the gap between ice gained and ice lost is getting smaller. Between 1992 and 2001, the net gain was 112bn tonnes a year, the paper finds. This dropped to 82bn tonnes between 2003 and 2008.
Several other studies have measured net ice losses in the EIAS in years more recent than were included in this study, for example:
Some of the more recent studies use the CryoSat-2 satellite, which was launched in 2010. A paper published in July analysed the first three years of this data, and finds that between 2010 and 2013, West Antarctica, East Antarctica, and the Antarctic Peninsula lost 134bn, 3bn, and 23bn tonnes of ice per year, respectively.
In summary, this is one of many studies on the subject, and more work will be needed to fully answer the question. It does not, however, contradict any of the key findings of climate science.
It will take a number of other studies, both satellite and on-the-ground research, to confirm if the new NASA study is correct about East Antarctica. If it is confirmed, it will still only apply up to 2008, not to the present day.
As Prof. Richard Alley states:
What is absolutely obvious is that this does not in any way mean that we don’t need to worry about sea level rise from our warming.