Method for parsing floats and adding totals
The add method is overly complex for no real benefit. It is hitting a thumbtack with a sledge hammer. The add method is used for waaaay to much. It's not clear what it does. I had to spend 5 minutes dissecting what it did. For an 11 line method, that's pretty long.

I understand you are trying to DRY up your code, but you have sacrificed clarity for perceived duplication of code. Adding to the credit and debit totals appears to be duplicated code, when actually it is not. You are better off removing the add method and going for something explicit. What you do want to DRY up is the conversions of amount values to numbers, and perhaps some error checking.

Defining this inside your dateObject class makes ensuring arguments are numbers a quick one-liner.

var toNumber = function(x) {
    var n = Number(x);

    if (isNaN(n)) {
        throw new Error("Invalid number: " + amount);
    }

    return n;
};


Now, your addCredit and addDebit methods become explicit and easy to read:

this.addCredit = function(amount) {
    totals.totalCredit += toNumber(amount);
};

this.addDebit = function(amount) {
    totals.totalDebit += toNumber(amount);
};


The addLabel method flat out confused me for a good while because it delegated to the add method. As a general rule, avoid turning methods into a "utility belt" where they perform more than one task. It makes for confusing code that is hard to maintain and debug.

The addLabel method (as far as I can tell) becomes much easier to visualize and debug as well:

this.addLabel = function(label, amount, type) {
    var key = label + "-" + type;
    totals.labels[key] = totals.labels[key] || 0;
    total.labels[key] += toNumber(amount);
};


And now on to every programmers' favorite subject: naming things :)

You have a "class" called dateObject. Naming conventions in JavaScript dictate that "classes", or more accurately constructor functions, should capitalize their first letter. Secondly, your dateObject class does nothing at all with dates, and is confusing because JavaScript has a Date class. Crediting and debiting amounts has nothing to do with dates. I realize you omitted some code but consider renaming this class to something like Account:

function Account() {
    var totals = {
        totalDebit: 0,
        totalCredit: 0,
        labels: {}
    };

    var toNumber = function(x) {
        var n = Number(x);

        if (isNaN(n)) {
            throw new Error("Invalid number: " + amount);
        }

        return n;
    };

    this.addCredit = function(amount) {
        totals.totalCredit += toNumber(amount);
    };

    this.addDebit = function(amount) {
        totals.totalDebit += toNumber(amount);
    };

    this.addLabel = function(label, amount, type) {
        var key = label + "-" + type;
        totals.labels[key] = totals.labels[key] || 0;
        total.labels[key] += toNumber(amount);
    };
}