"sanctuary" just means NYC and other similar cities do not coordinate with immigration police and federal agencies on arresting illegal migrants or people overstaying visas. It doesn't mean we or any other city has infinite resources to accept everyone. This should have been a matter for the federal government, but Texas acted unilaterally in its decision which in my opinion was not right. Instead what should have happened is the federal government and Texas would have coordinated with (and paid from federal grants) other states and cities and distributed migrants to where there was capacity ready, and find out where capacity can be added. "Sanctuary city" doesn't mean NYC is ready to just accept 10,000 migrants in a week lol