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I'm not sure if this can be answered without the specific circuit diagram, but I'm hoping that it can, as the circuit in question is a very common one. My question is about a small battery operated (4.5 VDC) circuit that runs a small string of miniature led lights. There is a switch existing that allows you to choose between "on steady" and "on flashing". There are other like circuits that allow different modes of blinking, but my question for now is just on the simple "on" or "flashing" circuit. What I would like to know is if it is possible to connect a capacitor and/or a resistor to the output in order to make the lights blink very very slowly, instead of their normal flashing speed. Could it possibly be that simple?

You probably need an oscillator circuit. You will need to add "something" to the resistor and the capacitor. Without using a choke (inductor), you have many options, one of which involves a logic gate such as a NAND gate

Try the simple circuit using a single input (of the 8 available) of a CD40106B given by TI on their web site (CD40106B), figure 9.2.3.

The output of the CD40106B is limited (in current), so you may have to drive the string of LED by feeding the output of the CD to another transistor (the gate of an MOSFET( NMOS) , or to the base of a BJT (NPN) ). The said gate, or base, will then acts like a switch, opening and closing the current at the frequency given by the oscillatory circuit.

Other alternatives are to use a NE555 (but much more energy lost). You could also use an Arduino like MCU (with many easy to get demos for a "flashing LED"), but that is probably an overkill.

Erratum/precision: the CD40106B is not presenting NAND gates but NOT gates, Schmitt triggered, and there are only 6 such gates, not 8. Without the Schmitt trigger, you won't get a useful delay.