Yes, the U.S. tax code is complex, but much of it doesn't apply to average individual tax payers. And it's not like filing tax returns is a one-time deal. It's something most people do every year for 50 years or more. So, figure it out. If you have a new tax situation, learn about it. Your knowledge base will grow and what once seemed tricky (claiming income from stock sales, filing with partial-year residency in multiple states) will become easy.
And for goodness sake, don't under-withhold. Just don't do it. And if you do it, don't blame anyone when you owe money.
April 15th shouldn't be a bad day--unless you have a messy house and seven people coming over tonight. Better get to work!