As @Everyone said it's not regarding feasibility but it's matter of budget and absence of human rated space vehicle and components
Budget
Development of a fully autonomous
orbital vehicle to carry a two-
member crew into a low-Earth orbit
(LEO) has already begun. ISRO
sources said the flight is likely to be
in 2016. Government had allocated
950 million (US \$14.5 million) for pre-
project initiatives for 2007 through
2008. A manned mission into space
would require about 124 billion (US
\$1.9 billion) and a period of seven
years. Planning Commission estimates
that a budget of 50 billion (US
\$765.0 million) is required for initial
work on the manned mission during
the eleventh five-year plan (2007–
12). A project report prepared by
ISRO has been cleared by space
commission. In February 2009
the Government of India gave the
green light for the manned space
flight programme, due to launch in
2016.
Human rated vehicle
The failure of GSLV in 2010 one made in India and other imported from Russia made the human space program to loss it's momentum.
The NASA CCP human-rating
standards require that the
probability of loss on ascent is no
more than 1 in 500, and that the
probability of loss on descent is no
more than 1 in 500. The overall
mission loss risk, which includes
vehicle risk from micrometeorites
and orbital debris while in orbit for
up to 210 days is no more than 1 in
270. [2] Maximum sustained G-loads
are limited to three Earth-standard
g's
ISRO must ensure that these conditions are satisfied
Space accessories
ISRO has planned to make everything indigenouly instead of buying from overseas countries. So lots of research must done to ensure reliability
Radhakrishnan, however, said ISRO
already has a budget of Rs 150 crore
for conducting pre-project studies and
developing critical technologies including
environmental control, space suit,
reentry and crew escape system. The
rocket must have man-rating, he
noted.
And another important thing I think is training astronauts and ISRO is now building astronaut training facilities in Bangalore and still it's under construction and it will become functional by 2013