  Double white dwarf binaries with merger timescales smaller than the Hubble
time and with a total mass near the Chandrasekhar limit (i.e. classical
Chandrasekhar population) or with high-mass primaries (i.e. sub-Chandrasekhar
population) are potential supernova type Ia (SNIa) progenitors. However, we
have not yet unambiguously confirmed the existence of these objects
observationally, a fact that has been often used to criticise the relevance of
double white dwarfs for producing SNIa. We analyse whether this lack of
detections is due to observational effects. To that end we simulate the double
white dwarf binary population in the Galaxy and obtain synthetic spectra for
the SNIa progenitors. We demonstrate that their identification, based on the
detection of Halpha double-lined profiles arising from the two white dwarfs in
the synthetic spectra, is extremely challenging due to their intrinsic
faintness. This translates into an observational probability of finding double
white dwarf SNIa progenitors in the Galaxy of (2.1+-1.0)x10^{-5} and
(0.8+-0.4)x10^{-5} for the classical Chandrasekhar and the sub-Chandrasekhar
progenitor populations, respectively. Eclipsing double white dwarf SNIa
progenitors are found to suffer from the same observational effect. The next
generation of large-aperture telescopes are expected to help in increasing the
probability for detection by ~1 order of magnitude. However, it is only with
forthcoming observations such as those provided by LISA that we expect to
unambiguously confirm or disprove the existence of double white dwarf SNIa
progenitors and to test their importance for producing SNIa.
