Joshua Spencer sent the message in April 2019 adding "it's amazing what a crackhead will do for £100", I'm going to get her beat up."
Spencer, 25, of Eddystone Rise, Knottingley, admitted a charge of sending an offensive and menacing message at Leeds Magistrates' Court.
The court was told this morning how Spencer had been a ward council candidate for Knottingley in 2019, while his now-deleted Twitter account suggested he was the deputy chairman of the Normanton, Pontefract and Castleford Conservatives.
His friend who received the alarming message on Facebook after they got into a political debate over Brexit was so concerned that he blocked him and passed it to his MP for Leeds, Hillary Benn.
It was then passed to Ms Cooper's office.
He was arrested on April 22 and denied sending the message initially.
His laptop was later seized and when police spoke with him again in July, he said he could not remember sending them, describing them as "vile".
Impact statements were read out in court from Yvette Cooper, her daughter and from former office manager for the MP, Jade Botterill, about how the threat of violence had affected them all.
Mitigating for Spencer, Sheik Amin, said his client had written the message when he was angry, in poor mental health at the time and in drink.
Mr Amin said: "He accepts sending the messages to his friend and did not intend to get Yvette Cooper beaten up.
" He was just venting. "
Spencer was jailed for nine weeks he was also made the subject of a 10 year restraining order against Cooper and Jade Botterill.