Some issues modeling a "two terminal source" coupled to a differential amplifier in LTspice
In your circuit, a floating source won't work, because the current flowing out of one of the "Vin" source's terminals must flow back into the other terminal on the Vin source. But for this type of amplifier, you must supply a positive current to both terminals.  These currents must flow through the bases of the transistor to ground and be always present.  The amplifier actually measures the changes to these base currents.  

When perfectly balanced, each emitter resistor is seeing 0.5 ma (splitting your 1 ma negative current source).  Each 12K resistor will have 6 volts on it, so your output will be centered around +6V and your base voltage has to be lower than 6 volts our your transistor's VCB is back biased.  It obviously must also be positive with respect to the negative supply.  A pull up resistor, either to ground or to the positive rail, is required for bias current, and the input can only "float" between +6V and the negative rail.

You also have a current source in series with your voltage source.  You have to remember that in simulation world, current sources are infinitely compliant power supplies, and a current source is capable of providing its current at any voltage, no matter how negative or positive.  For this reason, a current source in series with a voltage source doesn't make sense unless you set up compliance voltage limits in the model; otherwise the voltage source wouldn't do anything in theory.  Best to draw in your constant current circuit.