Depends on the size of the nation, if little like Vatican City it could do it very fast, if big like USA or Russia never.
Actually the biggest problem is not the production of electricity but the transport of electricity.
Even if your super reactor produces infinite energy at no cost, you can't transport for free.
Most energy will be wasted over great distances, charge and transport batteries will be too much expensive.
You should also consider the problem of heat, how many cables do you need to transport energy all over the nation from a single source?
In fact now world is going to have numerous small power sources instead of big powerful reactors (solar panels, wind turbines, modular nuclear reactor).
Your idea could work, if we assume in future to transport energy with high temperature superconductors, we assume to have some futuristic batteries that can stock infinite amount of energy at low price, etc..
Another couple of things:
1) in many nations we burn trash to produce energy, even if your SRE is cheap, you still need to dispose trash, they will pay it to do, and you also produce energy, so it can be more convenient.
2) Nuclear reactor can also be used to produce fissile material for nukes, so nuclear reactor could be still used for that purpose.
Even if your SRE will replace all other power sources, we will still need Redundancy to protect against power failures.