What will happen if I take an item costing 3 soul hearts but I don’t have enough

You can get the following pickups to cross gaps:

• Ladder - Cross 1 gap spaces
• Lord of the Pit - Gives you the permanent ability to fly
• Hanged Man Tarot Card - Gives you the ability to fly for your current room only, one time use
• Transcendence - Like Hanged Man, only a permanent upgrade
• The Bible - Gives you flight when used for your current room only
• A Pony - Usable item that also gives you constant flight (added on Halloween update)
• The Pinking Shears - Usable item that separates Isaac's head and body, allowing you control of the head (essentially another version of the Bible as a usable item, with added benefit of a free "Super Meat Boy" for that room while your body attacks enemies)

Credit to Chris Rasys for mentioning the Magnet, which can pull items towards you from a short distance away. While not technically the same as crossing the gap, it serves the same effect for the purpose of retrieving unobtainable items.

In this case, where there's a rock right next to the gap, using a bomb will plug the hole. This appears to be fickle though, as I've had bombs just destroy the block and not plug the hole. It appears that you have to be pretty precise in terms of the bomb placement so that the blast is exactly horizontal/vertical to the block.

My original answer stated that this would not work, but I have discovered that is incorrect. Poo piles that Larry Jr drops will in fact drop items. So far I have only observed hearts and soul hearts, but I would assume that the drop rate is the same as that of any other poo piles. The piles will drop items if the player pops them or if Larry pops them.

It may be slightly impractical to farm items this way because if you shoot at the poo piles you risk hitting Larry and possibly killing him, and you have to get hit infrequently enough to make up lost health with item drops.

So, it seems that you are correct that you could eventually fill the heart meter with soul hearts, but it would probably take a very, very long time.