How does the resistor at the tail act as a current source in a differential pair?
An ideal current source has infinite output impedance (i.e. \$dV/dI = \infty\$). A real current source is equivalent to an ideal current source in parallel with some finite output impedance Ro. 

A current source in parallel with a resistor is equivalent to a voltage source in series with a resistor (source transformation).







simulate this circuit &ndash; Schematic created using CircuitLab

So the long-tail resistor in your circuit is just a non-ideal current source.







simulate this circuit

In the traditional vacuum tube version, V- would be a very large voltage and Re would be a very large resistance, so that the resulting current was correct but it was closer to the ideal of infinite resistance.