Could the government? Sure, if they wanted to. But there are some pretty big issues to deal with.
1) where would the money come from? Why should taxpayers in 2018 pay for something that happened in the 1800s? (Assuming you get the idea through Congress, which will never happen) In my case, my ancestors were in Europe in the 1840s—why would they be asked to pay for something in a country they never lived in?
2) the government didn’t own slaves – private farmers and plantation owners did. Why would the government be on the hook for paying?
3) who would you pay? Sure, some slave descendants can trace their lineage, but many, even most, cannot. How would you know who is to be paid? Down to how many generations? Suppose it was a mixed-race – white male married black former slave. Would they qualify? What about compensation for people who died in slavery? Etc.
4) There is no basis on which to calculate the dollar amount. Back then, there was not a free labor market, nor any idea of minimum wage. So on what basis could you calculate what is owed? It would be a wild-assed guess at best.
Bottom line – it’s utterly unrealistic in every way.