The reactor itself, is doable...
The amount of highly enriched uranium required to sustain criticality is not massive. Although it can be done with a few dozen kilograms (less if you use plutonium), you would never actually be able to build a reactor this small for practical reasons:
* More fuel is needed to extend the life of the core.
* Reactivity decreases as the hot fuel expands, so you need more fuel to compensate. Maybe even neutron reflectors too.
* If you want to start and stop the reactor, control rods are needed too.
* Coolant channels make the core larger to cool the core and extract useful heat,
* Optional instrumentation channels to measure neutron flux (can be done external to core).
* Optional neutron source to make start-up go quicker and easier.
Still, even with these limitations, a reactor weighing less than half a tonne is possible. The Russians built reactors weighing less than 300Kg, with thermal outputs in the tens of Kw, so it's certainly possible. If you need to scale up power output, you would need to design the fuel geometry to have a high surface area, probably go for some cermet fuel, use a high thermal capacity coolant (probably molten metal or salt), and you would really need to pump a lot of coolant through it. All of this pushes you in the direction of using a fast reactor reactor than a thermal reactor, and the molten metal/salt can be used at low pressures which means you don't need massive thick pipes, keeping size and weight down. Of course the problem arises in that to run the core at at least 1.5Mw (probably closer to 5Mw when accounting for thermal inefficiencies), you are going to need to extract a lot of heat from that core, hence the real problem.
...but the power conversion isn't...
The reactor is only one part of the system. You also need to take the heat produced by the core, and produce useful electricity and shaft power to drive your tank. Step one of that is a main coolant pump, which for the kinds of flow you are talking about, is already going to be at least the size of a washing machine. Then you need to take that hot flowing molten metal/salt coolant, and do one of two things:
If you use a high temperature Brayton cycle, then you will use a heat exchanger to heat some gas, run it through a turbine, then allow it to expand, and run it through a compressor before repeating the cycle. unfortunately, most gasses do not have a high thermal capacity, so your heat exchanger is going to be massive. No way it could be fit within 2 cubic meters.
If you use a lower temperature Rankine cycle, then you will use a heat exchanger to boil water then drive a steam turbine. Water has a high heat capacity, so the heat exchanger will be smaller. However in my experience, heat exchangers for a nuclear plant still tend to be at least twice as large as the reactor itself. 435
Furthermore, steam turbines are not small. It's difficult to find weight specs, but this source gives a craneage weight for an 1.5Mw turbine as 3.4 tonnes. You may be able to shave a bit off that with fancy materials and clever engineering, but I doubt you could get it down low enough for the system to weigh less than 2 tonnes.
Both of these would then need to reject the waste heat from the system. This would require forced air convective coolers on your tank. Calculating the size of these is non trivial, so I'm not going to comment on how big they would need to be.
...and safety is impossible.
We often make fun of safety for ruining our fun, but there is no point building a tank if the crew is dead 10 minutes after they roll out of the garage. Shielding this reactor in such a confined area is going to be impossible, and a 5Mw reactor would produce a non-negligible amount of radiation. The shield itself would probably need to be at least half a meter thick (probably larger), and may require it's own active cooling. I just don't think it's doable.
Conclusion
If you are desperate to have a nuclear powered tank, I would suggest the following options: - The tank is an ultra-heavy monster tank. At 100s or 1000s of tonnes of tank, I would suggest that scaling laws make nuclear power more viable. Of course, this raises other problems. - The tank is a smaller, unmanned drone tank designed for long term deployment. Smaller 300Kg systems are viable, so you might be able to make a smaller unshielded drone. It's still not going to have a fantastic power to weight ratio, so the only advantage to going nuclear is if you want something that can operate without re-fuelling for long periods. - Artistic licence. 435