Just to complement the other answers: This isn't really about Kirchhoff's law. Rather, it is about an idealised situation that does not have a solution at all.
When you draw such a diagram, you can think of it in two ways:
- As a sketch of a real circuit. Then the voltage source is, e.g. a battery or a power supply, and the line is a wire. You can connect them this way, and something will happen (possibly, something will break or catch fire).
- As an idealised circuit. Then the voltage source maintains a fixed (presumably nonzero) voltage $V$ between the poles and supplies whatever current is necessary. The wire has no resistance, inductance or capacitance -- it will carry any current and produce zero voltage drop. You immediately see that you cannot satisfy both conditions. Hence, this idealised circuit does not admit a solution.
UPDATE
To extend this a bit: You can approximate the behaviour of real devices with combinations of ideal circuit element. For a battery, a common way is a series conection of an ideal volatge source and a resistor (see e.g. wikipedia), and a real wire would be an ideal wire with, again, a resistor (and possibly inductance and capacitance, see wikipedia again).
So in your case, you would have to include two resistors: An internal resistance $R_\text{int}$, which you can think of as part of the battery, and a wire resistance $R_\text{w}$, which really is distributed along all of the real wire and not a localised element.
The you wil have a current$$I=\frac{V}{R_\text{int}+R_\text{w}}\,$$ and an "external voltage", i.e. the voltage aong voltage source and internal resistance, of
$$U_\text{ext}=V-I\cdot R_\text{int}=V\left(1-\frac{R_\text{int}}{R_\text{int}+R_\text{w}}\right)\,.$$
In the fully idealised case $R_\text{int}=R_\text{w}=0$, these expressions are ill-defined.
You can look at two posible limiting cases:
- "Superconducting wire": If $R_\text{w}=0$ but $R_\text{int}\neq0$, i.e. superconducting ideal wire shorting a real battery, current is limited by internal resistance and external voltage is zero (and the battery will likely overheat).
- "Real wire on ideal battery": If, on the other hand, $R_\text{int}=0$ but $R_\text{w}\neq0$, current is limited by the wire resistance, and the external voltage is just $V$.