A couple of things. I haven't used the past couple of updates of Meteor so maybe 'User' has been added as a cursor to update the current user but from my experience this is how you would update the current user:
Meteor.users.update( Meteor.userId(), { $set: { 'profile.first_name': "example" } } );
Also note how I had to specify 'profile.first_name', in your snippet you would be trying to set first_name and last_name in the base of the user object when users are only allowed to edit the profile section client side. Lastly I'm not sure what 'this' is in the context of your Template so I would set currentUserId = Meteor.userId(), a convenient way to get the current user's id.