There has been plenty of attempt to blame Trump and changes to NOAA and NWS funding -- nearly all of which has not yet gone into effect -- for what happened in Texas. Indeed because of the impending inclement weather both in Texas and off the East Coast it has been reported that the NWS was running with extra personnel monitoring the weather situation.
While the facts are not all in these claims trying to blame Republicans and Trump specifically are almost-certainly not only wrong they're deliberately false.
First, in the "modern era" there are few places that get no cell service -- but such places do exist, particularly in low-lying areas where a natural formation is between you and the nearest cellular tower. Places subject to flash flooding often include those formations; box canyons are the most-obvious, of course, but hardly the only ones. Go into the Grand Canyon and you don't have to go very far below the rim before you lose signal, simply because there's a big hunk of rock between you and the transmitter.
NOAA also operates a weather radio system on VHF FM that broadcasts, but again if you're where you have something solid and impervious between you and the transmitter it won't alert for the same reason. These are inexpensive and will alert -- if turned on -- they're typically available in line-powered with battery backup configurations for about $50.
