  We examine the self-consistency of laboratory and observational data for
potential carriers of the 3.3 $\mu$m infrared emission feature (IEF), a member
of the ubiquitous family of strong interstellar IEFs at 3.3, 3.4, 6.2, 7.7,
8.6, 11.2, and 12.7 $\mu$m. Previous studies have shown that most Galactic
sources (reflection nebulae, HII regions, and planetary nebulae) show 3.3
$\mu$m IEFs displaying similar central wavelengths, full widths at half
maximum, and profiles. Our study is focused on the band profile designated as
Class A, the most prevalent of four classes of observed band profiles. In
contrast to the observations, laboratory spectra for gas phase polycyclic
aromatic hydrocarbons (PAHs), the widely assumed carriers of the IEFs, display
central wavelength shifts, widths, and profiles that vary with temperature and
PAH size. We present an extrapolation of the laboratory band shifts and widths
for smaller PAHs ($\le$32 carbon atoms) to the larger PAHs ($>$50 carbon atoms)
that are thought to be the IEF carriers. The extrapolation leads to tight
constraints on the sizes of the putative PAH carriers. Reconciling the
observations with the implications of the laboratory spectra pose a significant
challenge to the PAH and other IEF carrier hypotheses.
