No, unfortunately the tenant has no legal right to borrow from or against the security or any other deposits. Once you submit the deposit, it is held for your benefit, but you do not have any control over it. Certainly, you could ask the landlord to let you borrow money (whether against the deposit or otherwise), but that is completely at the landlord's discretion--they are under no obligation to loan you anything.

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The other attorney is correct that you generally do not have a right to borrow against security deposit.  However, your description raises an issue of whether the landlord took an excessive amount of security deposit from you.  You did not specify which city you reside in, so I can not tell if any local rent control laws may apply to you.  Looking at general California law, Section 1950.5(c) of the California Civil Code limits "security deposit" amount to two months' rent (for unfurnished residential property) or three months' rent (for furnished residential property), unless there is special circumstances (e.g. tenant will have a waterbed, landlord will be doing alterations at tenant's request, landlord and tenant agree to a larger deposit amount, etc.).  Please be sure to consult your own attorney to protect your legal rights.