The union, which represents about 2,000 customer service, on-board service and maintenance workers at the railway, and Via have set a deadline of June 14, 12:01 a.m.
"We're bargaining right through until the 14th," said Bobby Orr, assistant to CAW president Ken Lewenza.
The union served 72-hour strike notice on Monday, but will not be in a legal position to walk off the job until June 14 following a manadatory cooling off period.
"We've never had a strike here and we're going to work as hard as we can to get an agreement, but it's got to resolve the issues that are important to us," Orr said in an interview.
Contract talks have been ongoing since October.
Union members voted 94 per cent in favour of a strike if necessary.
After participating in talks on Monday, Lewenza said the high strike vote reflects frustrations and insecurities felt towards VIA.
"This is a direct result of a drop in federal funding and VIA’s so-called 'modernization' plan which has seen routes cut, stations closed and de-staffed. This plan is not the path to modernizing Canada’s passenger railway services."
Note to readers: This is a corrected story. An earlier version based on a CAW release incorrectly stated that the union would be in a legal strike position June 6.