WASHINGTON — The White House asked Congress on Friday for $44 billion in additional relief in response to this year’s devastating hurricanes, but facing rising budget deficits and pushing a tax cut that could cost $1.5 trillion, the administration also suggested that lawmakers make spending cuts to offset disaster costs.

Republicans have been conspicuously quiet about the ballooning national debt as they press to enact deep tax cuts before the end of the year. The deficit for the 2017 fiscal year totaled $666 billion, an increase of $80 billion from the previous year. And spending continues to climb.

Disaster relief costs are now approaching $100 billion, with more likely to come. And congressional leaders are eyeing a deal that would allow nondefense and military spending to burst through strict caps put in place in 2011, when Republican leaders made fiscal rectitude a central organizing principle.

The latest disaster request seemed to indicate that deficit concerns may be rising, at least in the White House. Administration officials laid out a menu of options for budget cutting, totaling $59 billion, from small nicks like $8 million from a rural energy program to far larger options, such as $3.9 billion from student financial aid and $1 billion from transportation infrastructure funds.