Well... you can. It's 29km (say 20 miles) but rather up-hill.
I don't know how well your fysical condition is, but for a first day... it can be done, but it also can be hard.
What I did was... start from SJPdP and walk 8km to the hostel (which cost a little more than the refugio in Huntto... 5km from SJPdP) and that worked for me.
A little 5 or 8km the first day to get used to climbing and the day after have a trip of 24 or 21km.
But I would most certainly NOT take a tent with you for 1 day, this case... from SJPdP tot Roncevalles.
Even if you want to walk the complete 29km (and start early in the morning)... if you take enough rest and listen to your body, you will make it... even with happy feet