Sure it does...it's in the Preamble. Try reading that.
Bush SOTU ping
We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.
I guess that's where the term "welfare" comes from. But notice it says to promote the general welfare, it doesn't say to "provide" the general welfare.
I don't see anything about public entitlements in those words (or anywhere else in the US Constitution.
Now, I guess if the preamble is interpreted as loosely as the Bible is to suit political ambition and agendas, then sure - it says the government is suppose to give entitlements to everyone, other than those who actually work for a living. Including those who are not even US Citizens, and are not here legally.