My wife is from canada, and I'm from the US, we got married in August. She only has her passport but we do go back and forth to CA and the US. But way

She should not cross the border without a green card.  There is a risk she'll be detained and deported since she is no longer allowed to travel without an immigrant visa now that she is married to a US citizen.  Once she obtains her green card, she will be able to apply for a social security number.