Voltage drop in a conductor
What's your conductor? Copper? Aluminum? 

The conductivity of these materials is well known. Copper is \$5.96\times 10^7 {\rm \frac{S}{m}}\$. It varies a little depending on temperature and how the metal was worked.

The resistance of a round wire is easy to calculate from the conductivity of the material, \$R=\frac{l}{A\sigma}\$, where \$A\$ is the cross-sectional area of the wire, \$l\$ is the length of the wire, and \$\sigma\$ is the conductivity of the material. So for any given length and diameter of round copper wire, you can calculate the resistance. Let's say 1 km of 10 mm diameter. Then you have
$$R=\frac{(1000\ {\rm m})}{\pi (0.005 {\rm m})^2(5.96\times 10^7\ {\rm\frac{S}{m}})}=0.21\ \Omega$$

And the voltage drop along the wire is given by Ohm's law: \$V=IR\$. So if you have 1 A flowing through this wire, 0.21 V drop. If you have 100 A flowing through this wire, 21 V drop. Whether that's significant or not depends on the voltage being used. 21 V drop on a 50 kV transmission line is pretty small potatoes.

There's a lot more to it than this, like aluminum is a worse conductor on a volume basis, but generally better on a dollar basis; and skin effect increases the effective resistance if you're using high frequency AC; and in an AC power network you can use transformers to trade off the operating voltage with the current while still delivering the same power to the load; etc.

Put this all together and the answer is, yes, it can be an issue. The guys who design power transmission lines have to choose the wire diameter (in relation to all the other system parameters and requirements) to avoid it being a problem.