Mark Sands (pictured below) from Upperton Gardens in Eastbourne admitted at an earlier hearing to a charge of "sending via electronic communications a message that was grossly offensive" to the representative for Eastbourne and Willingdon, Caroline Ansell.
In a statement, Mrs Ansell said: "I do not have any anger towards Mark Sands for what he has done, but many people in public life, particularly women, have to contend with similar abuse and threats on social media sometimes every day, and it is time it was stopped.
"On that basis, I do welcome the court imposing a prison sentence today."
Brighton Magistrates Court heard how Sands, a factory worker, wrote on Facebook: "If you vote to take £30 off my money, I will personally come round to your house... and stab you to death."
His lawyer, Madeleine Priestly, said her client had wrongly thought Mrs Ansell had voted for a cut to disability benefit which would have affected his income.
She described the comment as the "mistake of his life", adding that Sands suffered from anxiety and had a "high-functioning autism spectrum condition".
District Judge Christopher James said: "It was clearly designed to instil fear in her and it has succeeded in that intent by unsettling and unnerving her deeply."
Sands was also handed a restraining order, stopping him from contacting Mrs Ansell.