WASHINGTON—The House is back open for business. But getting legislation through it—much less agreeing with the Democratic Senate and President Biden—won’t be easy for brand-new Speaker of the House Mike Johnson, with major deadlines less than a month away.

After 22 days of GOP infighting, the Louisiana Republican secured his post Wednesday without any opposition from his fellow House Republicans. That unity will be tested soon, with lawmakers facing a slew of policy and political challenges, including a government funding deadline in three weeks, aid requests for Israel and Ukraine and a farm bill that has already expired.