Coventry City Council have warned that there could be 800 further job cuts and that it will be impossible to avoid this impacting on public services.
The City Council say it needs to find £26 million to balance its books next year, an increase from £14 million.
Emails were sent out to some City Council workers telling them their jobs are at risk. Richard Harty, UNISON says the news is "disappointing" after 700 people already having lost their jobs over two years to receive an email teling people there are more cuts to come.
More top news
He demanded the money after placing a carrier bag containing what appeared to be a heavy object on the counter.
Closures will be in place on the Aston Expressway, Park Circus and Salford Circus. There will be some full weekend closures and diversions.
West Midlands Police have said specially trained police negotiators are speaking with the woman to try and talk her down to safety.