The XP system has been changed since this answer was given. Now you gain 20XP per day survived, regardless of how many days have passed. This means that now, to unlock every character up to Wickerbottom it takes 64 days. The detailed XP requirements for each character are the following:
- Wilson: starting character;
- Willow: 160XP;
- Wolfgang: 320XP;
- Wendy: 640XP;
- WX-78: 960XP;
- Wickerbottom: 1280XP.
At the moment of this update there are also two additional characters, but they're not unlocked with the experience points, but by playing the Adventure Mode.
OLD ANSWER (Kept for historical purpose):
No, 35 days are not enough to unlock every character.
At the moment of this answer there are 6 available characters, and there's a level cap of 10000 XP:
In the wiki there's a table explaining the experience gains:
As you can see, the more you survive, the higher is your XP reward.
Each character after Wilson has an increasing xp requirement to be unlocked: Willow at 200 XP, Wendy at 1500, Wolfgang 3000, 6000 for WX-78 and finally 10000 for Wickerbottom.
So to unlock each and every one of them you have to survive 68 days.