I definitely believe the timelock can be accelerated. Though I can't think of any movies off the top of my head having just woken up, there seems to be plenty of instances where there's a set timelock and then somebody attempts to resolve the issue unwittingly exacerbates the problem.
In fact, in The Far End of the Black, the timelock is getting the needed antigen for the partial anti-dote that's inside "Faith," the scientist who has inoculated herself with the deadly virus. There's all sorts of real-life science in it, but the short story is the virus is predicated on "the death-switch" for program cellular death (interesting video here.)
In short, programmed cellular death is what is being done when doctors inject the polio virus to attack and kill brain tumors. In this case, it went wrong and causes cellular death (think gangrene from the inside out), resulting in something akin to a zombie.
In the story, (fresh) blood slows the effects of the virus - hence the need for blood sacrifice to ultimately save humanity (it's essentially the theme of the need for cellular death to occur - and how it does so naturally - to produce new, healthy cells on a larger scale). So the timelock can be delayed, but with consequences and there's only so few options.
To make it more interesting, I made the cellular regeneration rate slower than the cellular death rate - but there comes a "turning point" where the regeneration effect of the blood wears off and the death of cells accelerates as if making up for lost time. I liken it to watching a fire in a skyscraper - you can only give it so much water in an attempt to contain it before the building just crumbles (think of the Twin Towers.)
I think the key is in the approach of your story and how one peppers it with details that continually tug and pull at the expectation that has been set up. An example in real life can be seen in football: a team driving in the final seconds may have an option to kick the field goal to tie the game. Making it would delay the timelock and send the game into overtime, but one wrong move would also result in a ten second run-off.
Always look at potential consequences that can tighten those gaps in time - they often seem to result in doing something that, at first, seems to help but ultimately hinders.