Sorry for the length, but please bear with me. This is simple. And it may give some insight into what all the hullaballoo is all about. (disclaimer: I am not a tax expert except as an informed payer of taxes)
There are two separate issues to consider (and I'm sure you're aware of these, but just to clarify so that all readers are on the same page...believe it or not, some people don't understand these points):
(1) what your Federal income tax bill actually is. For example, line 15 on form 1040 (and equivalent on 1040A and 1040EZ, etc). Regardless of how it's paid, this is your tax due. This may have been pre-paid in full (or more) or in part through payroll income tax withholding, quarterly estimated payments, etc.
(2) then there's your tax "refund". Many people pay more in withholding on their jobs, etc, than what they will actually owe in income tax. This may be by intent or not. Some people like the forced savings of large withholding, others strive to have their withholding pretty well match their tax liability. Many people get their tax refund and get excited! They will go spend it on a trip or whatever.
Now what has happened with the 2018 income taxes is this:
(1) in most, but not all, cases people may have a lower tax liability. There are some losers on this though. Many itemized deductions have been capped or eliminated, and standard deduction has been increased. Personal exemptions no longer exist. If someone in the past had itemized a large amount for deductible mortgage interest, property taxes, and other taxes, etc, well, now they may not be able to itemize and they'll be taking the (now larger) standard deduction, with the result that their taxable income is now higher.
Conclusion for (1): most people will pay less tax but some people will end up paying more.
(2) The IRS tinkered with the withholding tables (for payroll deductions, not applicable to retirees) and in some cases workers may not have sufficient withholding to cover their taxes and they may owe additional money instead of getting a refund. Even if sufficient tax was withheld then due to the lower tax liability they may end up getting a smaller refund than they have in the past.
The IRS and numerous publications hammered on this all year long (2018) that workers should check their withholding to ensure that it was sufficient. No one should be blaming the government or IRS if they hadn't done this.
Retirees who made their quarterly estimated tax payments are *probably* okay (just guessing).
Conclusion for (2): so, the likelihood of you getting a refund, or owing additional cash, will depend on how good you "guessed" at your 2018 tax liability with your payments throughout the year.
I'm going to hazard a guess that a new retiree (for the full year) and who made proper quarterly estim tax payments will likely get a small refund or have a small payment due. It won't be the sort of catastrophe you've heard about.