The general consensus is Borderlands 2 is much tougher than the original Borderlands so you're going to have to step up your game if you hope to survive. The most significant difference is you can no longer carry health packs in your inventory. Instead you'll have to either find random loot drops of health packs (Health Now!), purchase them at a Zed's Meds vending machine or rely on special weapons or gear to replenish your health.
Fight For Your Life & Second Winds
If after doing your best, the enemy forces still manage to wipe out your shield and then reduce your red health bar to zero, you'll be thrown into the 'Fight For Your Life' mode. This is a short period of grace that lasts about 15 seconds. If during this 15 second countdown period, you manage to kill an enemy (any enemy), you will get what's known as a 'Second Wind' which will return you to normal play mode with about 25% of your health bar restored.
While in the Fight For Your Life mode, you can only move very slowly and you cannot scope or aim down the iron sights of any weapon and you cannot swap weapons from your backpack into weapon equip slots.
You can however turn to target any enemy you see and you can switch between any equipped weapons. So the best thing to do (and do it quickly) is to equip your best weapon and then look for the weakest enemy and go at him hard.
Sometimes if you're extremely low on health and you have enemies in the area that you know you'll have no problem killing, it may be to your advantage to let yourself get killed and then kill a weak enemy thus restoring your health bar to 25% of its capacity. This is a risky but effective strategy to regain some health.
Death Tax and Health
If you go into the Fight For Your Life sequence and you cannot successfully kill an enemy before the 15 second timer expires, you officially 'die' and the game will 'reconstruct' (respawn) your character at the nearest New-U station or the nearest map exit. You can think of New-U stations as game progress checkpoints which you uncover as you explore the gamescape.
Every time you die and get reconstructed, you'll be charged a 'death tax' which is essentially 7% of your current cash on hand. If you have no cash on hand or so little money that 7% of it represents a negligible amount, the death tax is waived and you'll get reconstructed for free.
The game starts you off with a maximum health bar capacity of 90. Every time you level up, your health is completely restored and your maximum health increases a little bit. It may therefore sometimes be to your advantage to tough it out with a depleted health bar if you know you're about to level up soon since levelling up will give your health bar a free refill.