Rep. James Bridenstine’s controversial nomination to head NASA faces mounting troubles, and the uncertainty threatens to further delay potentially major changes in agency programs favored by the White House.

For the second time in three months, the Senate Commerce Committee on Thursday is expected to narrowly approve the Oklahoma Republican on a party-line vote. His name never came up for floor action in 2017 because not a single Senate Democrat signaled support and Republican leaders were worried about rounding up the necessary...