Ottawa confirmed it was hoping to have completed the transfer by March 31 but last fall's provincial election delayed the plans.
The new tentative date for the transfer is Sept. 30 pending negotiations, said a spokesman for Quebec Health Minister Réjean Hébert.
On Saturday, more than 100 people attended a demonstration near the hospital, which is located on the western tip of the island of Montreal.
Families in attendance said they are concerned the quality of care might be affected by the transfer.
Workers said they are concerned the provincial government will double their workload.
One nurse told a CBC News reporter she is responsible for seven patients every day. She said "that's enough."
The hospital, which has 441 beds, will be merged with the West Island health and social services centre.
A similar rally was held last month, when the Union of Veterans Employees asked for a committee to determine the terms and conditions under which the hospital will be transferred.
The union group said there has been a lack of consultation during the transfer process.