Is it possible? Sure, but there are a TON of steps that would need to be taken first WAY before you could actually send anyone to mars. Your probably WAY better off setting up a station on the moon with mining equipment to help you build a bigger ship with more supplies (While you keep sending additional O2, extra soil and other supplies up to a space station to be stored) , then you would be using all the resources needed to get everything out of Earth's atmosphere.
In addition, setting up a sample "biodome" on the moon would give you practice and ensure you have what you need once you actually send a crew to mars (believe it takes about 2 years to get there). I don't think we have currently had any humans spend 2 years in space without coming back, nor have we even had humans live 2 years in a biodome without any outside resources being introduced. These are things that need to happen before you can send any manned ship to mars, and it's not something that can happen over night.
Best bet, in my opinion, work directly on getting comercial continuous flights up to a space station and back again (paid for largely by the passengers who are taking the trips), this would allow you to bring supplies up and constantly increase the size of the station (and more then likely build the actual ship in space that way). You could then, in theory, skip the whole moon phase (though long term it makes MUCH more sense to make a moon base first so you can send additional ships towards mars after the first.
Btw, doesn't have to be one way. Just because NOW we don't have a way to get them back, does not meen we wouldn't have one in say 10 years. We just need to make sure we have enough supplies/materials etc for the people who go to survive long enough for us to come up with a way to get them back.
If we where to figure out cold fusion for instance, say in 10 years, it would not be nearly as hard to make a ship that could make a round trip to mars.