Yes. Most 120volt outlets are 15 amps. A few in a house will be 20 amps: kitchen, dining, dedicated washer, and bathrooms(in houses wired after '96). So even a 120volt welder should have a dedicated outlet and circuit.
It's true, 99% of the houses wired the 15amp circuits will include many outlets in the house, and often in different rooms. The nature of building is to do the minimum required by code, since jobs go to the lowest bidder.. <img src="/forums/images/graemlins/pfft.gif" alt="" /> <img src="/forums/images/graemlins/pfft.gif" alt="" />
So unless you payed extra, or built an actual custom home with extra circuits and outlets, you will probably need to add a dedicated outlet for that welder. <img src="/forums/images/graemlins/mrt.gif" alt="" /> <img src="/forums/images/graemlins/mrt.gif" alt="" />