Dean's heart sank instantly at the words that his brother was bitten. His jaw tighten and the rest of what she said was nearly lost to him. He didn't make it. she said. No, he refused to believe it.
"Where are you?" He asked. "Tell me where you are and I'll come get you." It would be what Sam wanted and if he was lucky, he could either, find his brother's half eaten body or ... if he became one of them, he might be able to trap him and keep him from getting harmed till he could find something to save him.
Dean never gave up on his brother. Never wanted to give up on keeping Sam from being safe. Even if Sam, gave up on him.