  After the discovery of the Higgs-like boson by the LHC 2012 it is the most
important task to check whether this new particle is the Standard Model Higgs
boson or something else. In this paper, we study whether the 125 GeV boson
could be the pseudo-Goldstone boson of Little Higgs models. We derive limits on
the parameter space of several Little Higgs models (simple group and product
group models, with and without T-parity), both from the experimental data from
ATLAS and CMS about the different Higgs discovery channel and the electroweak
precision observables. We perform a fit of several Little Higgs models to all
electroweak parameters from measurements of SLC, LEP, Tevatron, and LHC. For
the Higgs searches, we include all available data from the summer conferences
in 2012 as well as the updates from December 2012. We show that there always
exists a region in the parameter space of the models under consideration where
the measured chi^2 is equal or lower than the SM chi^2: a closer look at the
minimum chi^2 will however reveal that the agreement with the collected data is
not significantly better as within the SM. While for the models without
T-parity the Little Higgs scale f is forced to be of the order 2-4 TeV in order
to be compatible with the collected data, in the models with T-parity the scale
f is constrained to be only above O(500) GeV, reducing the amount of
fine-tuning. We also show that these results are still driven by the
electroweak precision measurements due to the bigger LHC data
