No, 69 feet of sea level rise is not setting in, nor is the collapse of the West Antarctic Ice Sheet imminent. What is happening is that a couple of the West Antarctic outlet glaciers are imminently detaching from their grounding lines (i.e. the base of the glacier will no longer rest securely on the sea floor). Marine terminating glaciers are grounded under steady state conditions and detach from their grounding lines during periods of rapid advance or retreat.
The NYT article discussed two recent papers: An observational study that observed grounding line detachment in 3 major West Antarctic outlets; and a modeling study that examined the rate at which the portion of the ice sheet feeding the outlet would collapse after the Thwaites Glacier outlet became ungrounded.
The modeling study in particular is actually strongly optimistic. If your decision on whether to have children is based on climate science, then Joughin and others give you two good reasons to reproduce. First, they find only trivial additions to sea level over your children's lifetimes (about 2 cm over the next 100 years). Secondly, and more importantly, they find that the onset of rapid disintegration of this portion of the ice sheet is highly depended on how much heat we continue to put in the system. If we can keep melt rates minimal, they do not foresee this portion of the ice sheet collapsing during the next 1000 years. Under a high melt scenario (i.e. full steam ahead with global warming), they see ice sheet collapse within 2 to 3 hundred years.
Therefore, the future is up to us. And up to our children. We have not irreparably damaged West Antarctica. By controlling warming, we can control changes to ice sheets. And if you want to shape that future, one of the better ways to do so is to pass your values along to your children.
It's possible that Joughin and others are too optimistic. It's possible that we don't have hundreds of years to solve these problems. But the howls of agony and pronouncements of doom are getting rather deafening. And if liberals don't have children, our vision for a better world may well die with us.