Protection of endangered species is already something that the government is involved with and is partnered with other scientific groups and things to help them out. We should be very careful to not eradicate and entire species because we are lessening the biological diversity that we have on our planet.
Yes, the government should get involved with saving the lives of disappearing species, because this is not something that will happen on its own without government intervention. There are not enough people who have an interest in preserving these species that it will happen unless government steps in. They should help with this important job.
The government funds a variety of things, but generally science in general gets a decent chunk of money through grants. I believe grants are a good way to fund such a problem. Endangered species should be protected and the government should offer some funding in attempting to save these species.
While it's true that 99 percent of all species to have ever lived on earth are extinct, we should intervene to save species. Reason being? Because now we're the one who is wiping other species out, and it's ruining the planet. Having one species dominate and kill is very dangerous.