President Trump and his allies in Congress may soon have to recalibrate their strategy for a successful September now that the destruction caused by Hurricane Harvey has added another major item to an already long legislative to-do list.

Both Republicans and the White House have expressed a desire to move as quickly as possible to approve a wave of disaster-relief funding for hurricane victims when members return to Capitol Hill next week after a month-long recess.

But the next few steps are far less clear. Trump refused on Tuesday to walk back a threat he made before the storm to advocate for a government shutdown if Republicans fail to secure funding for the border wall.

And the White House hasn't yet signaled whether it will push to require spending cuts that offset additional Harvey relief money, which could complicate the process by inviting Democratic opposition.

"The president has made clear his commitment to the survivors of Hurricane Harvey in Texas and Louisiana," a White House official said in a statement provided to the Washington Examiner. "The administration is fully committed to working with Congress to help address the terrible destruction caused by this catastrophic storm."

The White House did not respond to a request for comment on whether Trump plans to donate money from his personal fortune toward the recovery efforts.

Texas Sen. John Cornyn, the Senate's second highest-ranking Republican, said Wednesday that the Trump administration seems "sympathetic" to the idea of moving quickly to pass a supplemental spending bill that would provide an immediate injection of money for Harvey before grappling with the particulars of larger spending legislation.

Lawmakers must either pass an omnibus bill that funds the government for the next fiscal year or a stopgap bill to buy a few more months for debate before the government runs out of money on Sept. 30 in order to avoid a shutdown. Some members have suggested a stopgap bill, which is known as a continuing resolution, is the more likely measure to emerge from next month's discussions.

Allowing the government to close in the midst of a robust federal recovery effort could jeopardize a massive operation and affect millions of people. Many Republicans had resisted the idea of a shutdown over fear of a backlash even before the storm rolled into Southeast Texas and raised the stakes of the spending fight.

The urgency of Houston's situation could shift the calculus among congressional Republicans who may have otherwise entertained a more aggressive fight for the border wall.

For example, Rep. Mark Meadows, chairman of the conservative House Freedom Caucus, said earlier this week that he believed many of his members would support a continuing resolution that would keep the government open past September even if it did not include appropriations for the wall. The North Carolina Republican suggested the Harvey recovery situation could even delay the border wall fight until December or early next year.

White House press secretary Sarah Sanders said Wednesday that the administration is still weighing whether to tuck Harvey relief funding into a continuing resolution or push for a separate appropriations bill.

Including Harvey funds in the stopgap spending bill is seen as a riskier move than pursuing the relief money through a separate bill because the continuing resolution could contain a large number of items that cause partisan fighting. Disputes about whether to fund projects or programs that have nothing to do with Harvey relief could slow down the approval process for recovery resources if lawmakers decided to tack relief funding onto the continuing resolution.

And tying relief funding to the stopgap spending bill would make any attempt to include money for the wall in that legislation politically risky, as Trump and Republicans could face criticism for exploiting the storm to push through a controversial measure.

Beyond relief funding and spending legislation, members must also vote to raise the debt ceiling before Sept. 29, when the federal government's authority to borrow money expires.

Trump has demanded lawmakers take up tax reform when they return to Washington next week as well.

"I don't want to be disappointed by Congress, do you understand me?" Trump said Wednesday at a rally in Missouri held to roll out the framework of his desired tax plan.

The president has grown increasingly frustrated with what he perceives as Republicans' refusal to execute the agenda he promised voters. Trump spent much of the August recess trading barbs with members of his own party and casting blame on congressional leaders for failing to repeal Obamacare last month and neglecting the debt limit increase until after their month-long break.