What is impeding current when voltage is stepped up in a transformer?
Nothing is 'impeding the current' in a step-up transformer. If you drive a low resistance load on the output, it will draw a large current.

The action of a good transformer is to tend to equalise the Ampere.Turns product in the primary and secondary, in an ideal transformer they are equal. 

The primary of a step-up transformer will have fewer turns than the secondary, so whatever current the secondary is providing, a correspondingly larger current will be drawn by the primary.

Ultimately, if you short circuit the secondary, then the current will be limited by the resistance of the windings (both primary and secondary, and connecting leads), the output impedance of the source, and in a non-ideal transformer its leakage reactance (the inability to have an infinite permeability core, or the windings in physically the same space rather than simply close). However, because of the ratio of turns, the secondary current will still be smaller than the primary current by approximately that ratio.