One of the first things I worried about when I started on my modern day Call of Cthulhu campaign, is:
-Cellphones, the players can simply call for help at any time
-Vehicles, why don't they just leave?
-Again, they can just leave if things get too dangerous
This is something that you'll probably run into, regardless of time or setting. You'll want to slowly build up the sense that the players are caught in a web, and now they can no longer escape. An integral part to that is the stakes. If the players have an important reason to see their mission through to the end, then they will not leave. And consequences to their actions are also important. If they call for help, they put more people at risk. You could artificially rob them of any means to escape the threat, but having strong stakes and consequences is better.
Now what I did in my story, was present them with a city that was slowly moving forward in time. There was an invisible field of some sort, created by a time machine, and had displaced the city in time. This displacement slowly got worse and worse. So at first they only felt a shiver as they entered the city, but as the days went on, leaving and entering this field became more dangerous. Making phone calls suddenly became part of the horror, as they first started receiving answers from the future before they had asked the questions... and later they started receiving calls from another world, and they became afraid to answer the phone. They also started seeing figments of future events, and interactions with people from the future (which they believed to be ghosts at first).
The players also had a car, which broke down when the players crashed into their first clue, right at the start of the campaign. The story did not hinge on their vehicle breaking down, but I wanted them to feel vulnerable. I described how the car drove through a puddle, which ended up being a lot deeper that it seemed. The car struck a concrete tube hidden underneath the road, and thus broke down. Right away the players were stuck in town, with a mystery to solve.