Menzie Chinn shows us the various estimates from GDPnow (Atlanta Fed), e-forecasting, and Macroeconomic Advisers
I thought I'd put a prediction out there using this model (which estimates RGDP per capita [prime age], so this includes an extrapolation from the model plus an estimate of the prime age population growth with the errors propagated from each but nearly all of the error is in the RGDP model by an order of magnitude). The result is (SAAR, chained 2009 dollars):
16,933.2 ± 63.9 billion dollars (1σ)
0.71 ± 0.38 % growth  ... i.e. 0.3% to 1.1%
Chinn tells us the Bloomberg consensus is 1.1%. Macroeconomic Advisers says 0.3%. GDPnow says 0.2%. The dynamic equilibrium model of RGDP per capita basically covers that entire spread. However, the dynamic equilibrium model has only two parameters (since were not in shock). That means that all the parameters of the GDPnow model or MA's model are getting you a just few tenths of a percentage point.
GDPnow seems to take into account the "low first quarter effect"; I wonder if MA does the same?
Update 28 April 2017:
The number is here and it is a bit lower than the model shows:
(+ 0.2 %)
which means Quarter/Quarter growth (that I show above) was 0.2% (and annualized is 0.7% which you might have seen in news reports e.g. here).
However, this is the advance estimate and there is a tendency for these to be revised (though it could be "low first quarter effect" mentioned above). So we'll see on 26 May 2017 what happens.
 Quarter on quarter SAAR. Based on the not-yet-revised 16,813.3 billion number for Q4 2016.