No, Yeshua does not speak against gov'ts helping people, but He definitely speaks (along with His Father) about people relying on (man) gov't over the Lord. That is what "welfare" does; it causes the recipients to have "faith" in gov't over the Lord (that would be directly against what Yeshua taught).
That's ridiculous. There is no evidence to back up your silly assertion.
If there are Christian individuals that have faith in government over faith in God I'd be interested in meeting them. And I'm sure they will squirm a bit trying to get past the pearly gates.
But your thinking reveals that YOU want the government to assure that people don't have faith in government over God and that is quite ironic.
In the time of Jacob's Joseph, there was a terrible drought. Instead of praying to the Lord or asking Him for help, Joseph's brothers were sent to Egypt (the gov't) to buy grain. They went back until they had no money. When they had no money, they took their possessions, and traded their possessions to the gov't for food (they did not rely on the Lord). After their possessions were gone, they had nothing left for food, what did they do? They sold themselves into slavery (willingly) to the gov't for food, instead of asking the Lord. They were slaves for a very, very long time before Moses was sent by the Lord (who they remembered once their suffering as slaves became constant).
Rely on the gov't for food and end up a slave. Rely on man over the Lord and end up being kept by those you "trusted".
Yeshua would tell His disciples that they were thinking of this world, and not of His world when they were discussing the "greatest among them". He explained that "serving" their fellow men was what He wanted them to do (notice nothing about being a great gov't, confiscating others' wealth was mentioned). Yeshua had many, many followers, none of them were told to become "community organizers" or gov't workers. The tax collecters that Yeshua dined with were encouraged to be honest (not follow the corruption of the gov't), and stop sinning. They were given the power of the Holy Spirit and could have used that power to build a nation. They did not. They used that "power" to give EACH person a relationship with the Lord to use, according to each individual's choice. There are other examples of where the disciples attempted to pressure Yeshua to use violence or His power to get what He wanted. He did not. He was the perfect sacrifice, a Lamb without flaw, that was tortured (there are people that claim He had over one thousand wounds from beatings and flogging), and for good measure a crown of thorns forced into his scalp, and murdered during passover so the Jews (and any that believed, right along with them) could be forgiven, and that sins would no longer be passed from generation to generation.