I have a Travel document with only 5 months validity. Can I be given a visa?

Manks
I'm a Permanent Resident from the United States. I have a travel document that is issued only for a year (1 year validity). Now I have only 5months left for the document to expire. I need to go to China urgently to see a sick family member. It takes about 5 months for another travel document to be issued to me by the US Government. I really need to go. Can the consular give me a Chinese entry permit so I can visit my sick family member just for 10 days?