Sure she can. Is it possible for you to go to a 24 hour pharmacy? They are usually open 365 days a year, so it doesnt matter what day your refill is due, she can tell them on friday to fill it and let you pick it up on saturday or sunday. I have to also wait until the day when I am completely out to get my refill, its just the way some doctors like to do it, but if you get up and go in the morning, you dont miss a dose.
I dont know why any doctor does this, My new doctor has me on an every 28 day refill, and it's so much easier. I know and he knows that every 4th tuesday, I am out of meds and need to pick them up. I call on mondays, then tuesday I pick up my prescriptions at his office and get them filled.
Some doctors are more strict than others, thats just the way it is, and a lot of them would choose not to help chronic patients at all if they HAD to keep us on our meds no matter what, They are risking their license to practice by trusting us with narcotics, and they not only have a right, they have a responsibility to cut someone off cold if they suspect anything isnt they way they want it.
I hope you can get on the 28 day thing, that really helped me, I hated when it was 'one month' sometime the pharmacy would make me wait 32 days so for 2 whole days I would have no meds.