Nothing will happen if your spouse doesn't want to file taxes jointly with you.
Your spouse has to give you joint consent to file a joint tax return with you.
Although Filing taxes Jointly does have a lot of great advantages but it's okay to file separately if you want too.
Now if your spouse doesn't file taxes at all then your spouse may be in trouble with the IRS after some time.
If your spouse isn't paying taxes or filing taxes it could get you into trouble with the IRS as well so I would advise speaking with the IRS about it.