Kevin Faulconer, the former Republican mayor of San Diego who is challenging Mr. Newsom in an upcoming recall election, said the rent relief program was only a temporary fix.

“One-time gimmicks are no substitute for permanent tax relief,” Mr. Faulconer said Monday. “California is unaffordable for middle-class families, that’s why they’re leaving our state en masse.”

Before the pandemic, housing and homelessness regularly ranked as the top issues for voters and last year the state lost population for the first time, as middle-class homeowners fled the state for cheaper housing elsewhere. While some of this was driven by one-time factors, the state has consistently seen more people leave than move in from another state over the past decade, and in the process lost a net of 900,000 residents to out migration. The issue has become so prevalent that bitterness about incoming Californians has stoked a backlash in cities like Boise, Idaho, where housing prices have jumped with the influx of newcomers with bigger home-buying budgets.

Worried that the pandemic would exacerbate what is already the state’s most pressing issue, California responded aggressively, passing one of the nation’s strictest eviction moratoriums and moving some 35,000 homeless Californians into hotels, a model that has proliferated nationwide. The governor has proposed spending $12 billion on homelessness, including $7 billion to buy motels and apartments to convert them into shelters and $1.75 billion to build affordable housing.

While government efforts have been key to keeping tenants housed during the pandemic, rental programs in California and elsewhere have been plagued with problems and slow to get the money out. Studies show that about a third of tenants have at some point used federal stimulus or unemployment money to pay their rent since last year, but a much smaller number, as low as 2 percent, have been able to access a rental program. Consequently, a majority of renters still had to borrow or draw on savings to cover bills during the pandemic, leaving them less able to weather future emergencies as the economy recovers.

On Monday, state lawmakers were working on a bill to extend the eviction moratorium past its June 30 expiration date, according to several officials in the Legislature who requested anonymity to discuss ongoing negotiations. A vote could come as early as this week. Lawmakers are expected to extend the eviction moratorium and cover 100 percent of the rent for lower-income tenants, up from 80 percent of their rent bill through current programs, the officials said.