They can if they sue you, but if the amount you owe is not a large amount they likely won't go that route. What they are more likely to do is send the file to a Collection Agency, which will impact your credit score. Your credit score is a big factor in future applications for credit, and is also a factor in the interest rate that you pay on future credit. Not sure what is causing your inability to make the payments, but you may find your best option is to contact them and try and work something out.
I work in Credit for one of the Big 5 banks, and worked in Collections for 4 years as well