You might check thew rules. Even for the day, you are suppose to have your 'papers' with you in the US. (Canuki ID)
I may be wrong....
For us, US Citizens. We now need to have a US Passport to return from a day in Tijuana.
I use my passport to cross over, but I'll be damned if I carry it into the river with me to fish..or on hikes, or shopping for that matter. The Border patrol doesn't provide me with anything when we cross. Mind you, I'm not there to work. They do have a digital record of my crossing (PP#, license plate#), which I'm assuming is linked with the cops so even without papers on me, I can prove that I crossed legally.
The only time I get stopped on the south side of the 49th is when they want to see my fishing license if I'm all decked out in my gear.*
*On a side note, the damned thing nearly doubled in price from last year. Went from $40US to $70US for an out of state license.