WASHINGTON — Facing what could be the most powerful storm to slam into the United States in more than a decade, President Trump and the team he has put in place at the Federal Emergency Management Agency were bracing on Friday for one of the most important tests of his presidency.

The stakes could be exceedingly high. Few events test the effectiveness of an administration — or bear as many political risks — like a major natural disaster.

The storm, Hurricane Harvey, made landfall near Corpus Christi, Tex., as a Category 4 hurricane late Friday. It is predicted to pummel the South Texas coast with winds exceeding 110 miles an hour and up to three feet of rain. After making landfall, forecasters predicted, the storm would make a turn back up the coast toward Houston, the nation’s fourth-largest city and home to the oil and gas industry.

Mr. Trump used the power of his preferred megaphone, his Twitter account, to signal to his more than 36 million followers on Friday that he was closely watching the storm, as members of his administration sought to project that they were on top of the looming crisis.