"We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, 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."
The second appearance of the word Welfare in the U. S. Constitution is in the introduction of Section 8:
"The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States"
The writers of the Constitution were well aware that these welfare clauses were vague, and many feared that they would be subject to abuse. Nevertheless, the words were left vague.
Liberals on welfare
Liberals understand these word to give Congress broad powers to help people in ways that benefit the whole nation. When liberals use the word Welfare, we generally use it to describe several social programs that provide goods and services or education to Poor people. Liberals use the term Entitlements to refer to programs that citizens have already paid for individually and are entitled to receive: Medicare, Unemployment, Social Security, Pensions, etc. Liberals use other terms like tax deductions, and subsidies to refer to other programs which are intended to promote the general welfare.
Conservatives on welfare
Conservatives understand these words to give Congress very limited power to help people in ways that benefit the whole nation. Ultra-Conservatives often believe the Constitution gives Congress no power to help people even if it benefits the whole nation. Most Conservatives, however believe the only acceptable welfare is tax advantages and subsidies for business and the wealthy, and the only acceptable entitlements are actual titles and social privileges given to rich people.
We American Liberals eliminated those conservative entitlements in a Hard fought revolution, and if conservatives don't like it, they can continue to suck up to Lord Koch, but we'd prefer they do it in some other country.