Named after Senator Patrick Toomey (R) from
Pennsylvania who is notorious for ignoring his
constituents (he held zero in-person town halls since becoming elected in 2016 throughout key policy discussions including the appointment of various cabinet members requiring Senate approval to debating health care legislation, and he received tens of thousands of faxes from
constituents who were unable to reach him using his email or phone), to toomey someone is to wilfully ignore them, especially in cases where it is one's job to pay attention to them.