You will probably be allowed in, but you will probably be spending a lot of time with the American immigration officer. What airport are you flying out of? If it is YYC, they don't allow you to enter the customs and immigration hall until two hours before flight time. I suggest paying to go standby on an earlier flight, and attempting to enter the hall on that pass.

At YVR, because the order of security and immigration is reversed for US bound flights, this two hour nonsense doesn't apply.