When one of the most stinging defeats of his short tenure arrived on Tuesday, Speaker Mike Johnson had put himself front and center in the House chamber, standing in front of the speaker’s ceremonial chair on the upper tier of the rostrum to gavel it down.

As Republicans tanked their own bid to impeach Alejandro N. Mayorkas, the homeland security secretary, Mr. Johnson, who minutes before had been buttonholing holdouts on the House floor, was the face of the failure, a slightly panicked look on his face and his cheeks flushed as he announced the loss.

Then the House moved on to a second vote Mr. Johnson had orchestrated, on a $17.6 billion aid package for Israel that he knew would not muster the votes it needed to pass.

It also failed.

The back-to-back defeats highlighted the litany of problems Mr. Johnson inherited the day he was elected speaker and his inexperience in the position, roughly 100 days after being catapulted from the rank and file to the top job in the House. Saddled with a razor-thin margin of control, and a deeply divided conference that has proved repeatedly to be a majority in name only, he has struggled to corral his unruly colleagues and made a series of decisions that only added to his own challenges.

Mr. Johnson on Wednesday was sanguine, painting the dysfunction that had played out the night before as the kind of messy democratic process the founding fathers had envisioned.

“The job will be done and we’re going to govern,” he told reporters just off the House floor. “This country is the greatest country in the history of the world. The entire world is counting upon us. We have steady hands at the wheel. We’ll get through it. Everybody take a deep breath. It’s a long game.”