Let's look at your title first: 'Does 'make' here a verb?' That's not quite right, is it? This is quite a simple construction, so I think you can correct this yourself. Now let's have a look at the sentence. Unfortunately that doesn't look right either. Are you sure that you copied it correctly? Should it perhaps say '... the number one New Year's resolution made is ...? Why don't you sort out your title and your question, and then come back to us if you still have problems?

"Make" is a verb here, but you've structured your question ungrammatically. In proper English we would write "It says that the number one New Year's resolution PEOPLE make is to spend more time with friends and family." Or, you could simply leave out "make" altogether in favor of "It says the number one New Year's resolution it to spend more time with friends and family." (In this case "people" would be understood). Finally, your question should be asked with 'is" rather than "does" --ie: Is "make" here a noun or verb?