"is it hypocritical to call myself a Christian and not support welfare programs?"
It looks like this question could be read at least two ways - first, should we support the creation of welfare programs (as opposed to finding other, privately-funded ways to help the poor)? second, should we support welfare programs that have been instituted (as opposed to, say, evading or petitioning to opt out of paying the tax that supports them)?
The second question--do we give our financial support to existing welfare programs if the government compels us to--is easy:
Mark 12:14-17 (NASB):
They came and said to Him, "Teacher, we know that You are truthful and defer to no one; for You are not partial to any, but teach the way of God in truth. Is it lawful to pay a poll-tax to Caesar, or not? Shall we pay or shall we not pay?"
But He, knowing their hypocrisy, said to them, "Why are you testing Me? Bring Me a denarius to look at."
They brought one. And He said to them, "Whose likeness and inscription is this?" And they said to Him, "Caesar's."
And Jesus said to them, "Render to Caesar the things that are Caesar's, and to God the things that are God's." And they were amazed at Him.
Of course this raises the question of whether we ought to 'render unto Caesar' things that are wrong and unjust, which brings us to our first question: Do we say that the government ought to support the poor? The Bible is mostly addressed to individuals, not governments. But there are a couple of clear cases where the rulers of cities and nations are addressed and expected to support the poor, such as Deuteronomy 15:6-8--
"For the LORD your God will bless you as He has promised you, and you will lend to many nations, but you will not borrow; and you will rule over many nations, but they will not rule over you. If there is a poor man with you, one of your brothers, in any of your towns in your land which the LORD your God is giving you, you shall not harden your heart, nor close your hand from your poor brother; but you shall freely open your hand to him, and shall generously lend him sufficient for his need in whatever he lacks.
--and Daniel 4:27--
`Therefore, O king, may my advice be pleasing to you: break away now from your sins by doing righteousness and from your iniquities by showing mercy to the poor, in case there may be a prolonging of your prosperity.'
Failure to do so when there are means to do so was the sin of the city of Sodom, according to Ezekiel 16:49:
"Behold, this was the guilt of your sister Sodom: she and her daughters had arrogance, abundant food and careless ease, but she did not help the poor and needy.
Now, if the welfare program is poorly conceived, the law poorly worded, the financial aspects poorly provided for, by all means, one could oppose implementing a welfare program on those grounds--but to do so only because it is a welfare program should certainly be un-Christian.
Of course the government giving its support to the needy does not excuse us from our personal obligations to charity. But the government itself does have this obligation as surely as we do individually.