Orsdxy

Pathogen

Note: For the purpose of this question I define a pathogen to include viruses and/or bacteria. Edit: I don't exclude other biological agents such as fungi that might have the same effect.

Pathogen

A pathogen or infectious agent is a biological agent that causes
disease or illness to its host.

https://www.sciencedaily.com/terms/pathogen.htm

Sometimes we hear of a potential threat to humanity from a 'killer' virus, for example bird-flu. https://www.webmd.com/cold-and-flu/flu-guide/what-know-about-bird-flu#1

There have been plagues that have killed vast numbers of people but none have resulted in actual extinction. https://www.mphonline.org/worst-pandemics-in-history/

HIV Aids, Bird-Flu and others have affected more than one species.

Question

In theory could a microbe arise that could completely wipe out an entire species (in particular humans) or more importantly all mammals (and maybe other species as well).

Clearly mammals have not all been wiped out so far because we are still around. My question is, could it conceivably happen given what we currently know? If not, what would prevent it?

Yes, but not in the way you are thinking.

One way this could happen is if some killer fungus starts growing unchecked throghout the planet, on land and sea. By killing all plant life it would destroy every other ecossystem, so it would wipe out all mammals. It would also practically wipe out all other members of the animal kingdom. This is part of the plot of Sid Meyer's Alpha Centauri.

Another way is if some methane-producing microbe starts spreading unchecked. This may have already happened:

The Permian–Triassic (P–Tr or P–T) extinction event, colloquially known as the Great Dying, the End-Permian Extinction or the Great Permian Extinction, occurred about 252 Ma (million years) ago, (...) It is the Earth's most severe known extinction event, with up to 96% of all marine species and 70% of terrestrial vertebrate species becoming extinct. It is the only known mass extinction of insects. Some 57% of all biological families and 83% of all genera became extinct.

(...)

Suggested mechanisms for the latter include (...) a runaway greenhouse effect triggered by sudden release of methane from the sea floor due to methane clathrate dissociation according to the clathrate gun hypothesis or methane-producing microbes known as methanogens.

And if methane won't do, bacteria may deplete the oceans of oxygen. Then:

A severe anoxic event at the end of the Permian would have allowed sulfate-reducing bacteria to thrive, causing the production of large amounts of hydrogen sulfide in the anoxic ocean. Upwelling of this water may have released massive hydrogen sulfide emissions into the atmosphere and would poison terrestrial plants and animals and severely weaken the ozone layer, exposing much of the life that remained to fatal levels of UV radiation. Indeed, biomarker evidence for anaerobic photosynthesis by Chlorobiaceae (green sulfur bacteria) from the Late-Permian into the Early Triassic indicates that hydrogen sulfide did upwell into shallow waters because these bacteria are restricted to the photic zone and use sulfide as an electron donor.

Yes, viruses and bacteria can infect multiple species, even not closely related. If a hypothetical pathogen, lets call it pigeon pox, mutates, and gains ability to infect some tissue or organ shared by all mammals e.g. placenta, and as a side effect it causes the death of a foetus, it can potentially wipe out all mammals in a generation. It will not be easily contained like ebola, because its main reservoir is still a pigeon. If it survives in female reproductive tracts after killing the foetus not only it is preventing any future pregnancy but may also spread among mammals directly as STI.
Pigeons will still be happily flying, coughing an sh**ting in our towns when we're gone because for them the virus only causes mild rash around cloaka.