Er, no. Quantum field theory and General Relativity don't appear to mix because a quantized spin-2 (read: gravitational) field can't be renormalizable (read: finite) in four dimensions. That's a mathematical fact that's independent of the value of the cosmological constant.
Which side are you on out of curiosity?
Extra dimensions. I believe QFT and GR are both correct. There is experimental evidence of the quantized nature of the gravitational field. If all that is the case, it implies that there are more dimensions than the four we measure.