  We consider reflection and transmission of 2D quantum wavepackets with phase
vortices (also known in optics as spatiotemporal vortex pulses) at potential
step-like, delta-function, and rectangular barriers. The presence of a vortex
significantly modifies the Wigner time delays and Goos-H\"{a}nchen shifts,
previously studied for Gaussian-like wavepackets. In particular, the scattered
wavepackets undergo non-zero time delays and lateral shifts even for purely
real scattering coefficients, when the standard Wigner and Artmann formulae
vanish. We derive analytical expressions for the vortex-induced times delays
and spatial shifts of 2D vortices and verify these with numerical calculations
of the Schr\"{o}dinger equation. The time delays and shifts are resonantly
enhanced in the vicinity of the critical-angle incidence for a step-like
potential and near transmission resonances for a rectangular barrier.
