Newly installed Speaker Mike Johnson is confronting a multitude of crises during his first days in office, chief among them a deadline just weeks away to avert a government shutdown and an urgent request from President Biden for a behemoth $105 billion aid bill for Israel and Ukraine.

They are two of the issues that have most bitterly divided the House Republican conference and helped lead to the ouster of his predecessor. Now it falls to Mr. Johnson, a fourth-term congressman who has never served in a top leadership position before, to try to keep his anti-spending party united and the government open — all in a matter of weeks.

The previous speaker, Kevin McCarthy, found it impossible to corral recalcitrant Republicans to pass legislation to keep federal funding flowing and prevent a politically and economically damaging shutdown. At the last moment, he turned to Democrats to push through a bill to extend the deadline through Nov. 17, a move that prompted hard-right Republicans to force him out.

Mr. Johnson was among a majority of Republicans who opposed that stopgap spending bill. He has also opposed continued aid for Ukraine for its war against Russian aggression, and he said on Wednesday that he wanted to see “conditions” imposed on additional U.S. aid.