We truly are fraught with contradiction.

Locke argues that the duty to labor comes from a right to self-preservation, which we do by following the laws of nature that urge us to take advantage of what is granted to us by God.  Locke writes in Chapter 5, Section 31:

That same law of nature, that does by this means give us property, does also bound that property too.  God has given us all things richly (1 Timothy vi. 12) is the voice of reason confirmed by inspiration.  But how far has he given it us?  To enjoy.  As much as any one can make use of to any advantage of life before it spoils, so much he may by his labor fix a property in:  whatever is beyond this, is more than his share, and belongs to others.  Nothing was made by God for man to spoil or destroy.  

 The laws of nature oblige us to labor in order to avoid "spoiling" God's gifts, while operating in self-preservation.  In its organization of people, societies inherently automate this process, and we learn that we must labor as part of preserving ourselves within that system. The mechanism through which we can preserve our individual selves within our society is by laboring, as Locke writes in Chapter 5, Section 35,  "The law man was under, was rather for appropriating.  God commanded, and his wants forced him into labor."  

 The obligation for the rich to provide some property to the poor arises from the second proviso of Exodus, "enough, and as much" condition to property acquisition.  The exchange of "enough" between the wealthy and the poor is contractual.  The wealthy are obliged to give; the rich man's ancestor may have been but a poor man who stumbled upon a plot of land and tilled it efficiently, building a substantial fortune over subsequent generations from this first act of labor.  The "Charity" given from the rich to the poor is equivalent to this first act of property acquisition by laboring, granting nothing but opportunity, over which the poor must labor, similarly.  This is where the poor person's end of the contract comes in, as the "Charity" is not a free ride for the poor, regardless of the particularity of the benefit.  Both parties give, one by charity and one by laboring over that charity; society is stronger for it.

 The "strong individualist" interpretation might warrant Locke to focus on the importance of the poor's willingness to labor, but he must, in turn, emphasize the obligation of the wealthy to provide the poor with the opportunity to labor for their own subsistence.  Each effort needs the other.  Both must make a living; the wealthy may continue to prosper by employing the poor.  In this mutually beneficial model, both are operating freely and pursuing self-preservation and prosperity.

  The "strong individualist" interpretation would still require state mechanisms to help each individual preserve her or himself.   The entire foundation of government is to help individual persons preserve their selves, and this happens through labor.  Government policies to help facilitate this process are not only necessary, but the absence of such supports would be entirely inconsistent with the purpose of government.  The government must provide work support systems - these are more consistent with Lockean philosophy than welfare benefits - that require beneficiaries to engage in work-related activities to preserve themselves. 

 In this way, being a strong individualist does not require writing off the social obligation, as the "strong individualist" and "social obligation" interpretations of Locke's arguments are not of mutually exclusive situations.  Locke would not oppose taxation to support a work-support system; in the same way that a vote in an election is consenting to the will of the majority (Chapter 11, Section 140), paying a tax to a government under which I own land is equivalent to giving up some natural liberty so that I can be preserved under that state.  My livelihood and my security would not be guaranteed without that system.  Both actions consent to and legitimate the government and society.  In this way both interpretations can be fused, for what is helpful in preserving each individual is also an act in preserving the common, societal good.  The price for this process is a tax: a social obligation that serves many different purposes.  Strong individualism and social obligation are tied together, creating a stable, functional society.