The full quote from Romney: "The mayor said -- and I quote almost verbatim -- which is 'if you happen to be in this country in an undocumented status - and that means you're here illegally - then we welcome you here. We want you here. We'll protect you here.'"
Romney is referring to a statement Giuliani made at a 1994 news conference: "If you come here and you work hard and you happen to be in an undocumented status, you're one of the people who we want in this city. You're somebody that we want to protect, and we want you to get out from under what is often a life of being like a fugitive, which is really unfair."
Romney says that shows Giuliani is too welcoming to illegal immigrants and that his policies made New York a "sanctuary city." We've addressed the sanctuary city debate in this item and this article, so we'll simply focus here on the quote.
Indeed, Romney accurately summarized what Giuliani said. The quote came from a 1994 story in the New York Times that was headlined "New York Officials Welcome Immigrants, Legal or Illegal."
The article noted that Giuliani had given a "spirited defense of illegal immigrants, virtually urging them to settle in New York City." It quoted him saying, "Some of the hardest-working and most productive people in this city are undocumented aliens. "
Giuliani has not denied the comment but, in discussing immigration, has emphasized the need for more border security and tougher enforcement by the federal government.
We find that Romney accurately described Giuliani's comment and find Romney's statement to be True.