The demand among renters who want to become first-time homebuyers is growing and millions are just waiting for favorable market conditions that increasingly are fading, according to the inaugural edition of the Zillow (Z) housing confidence index.

The existing headwinds include inventories that are too tight, mortgage interest rates projected to climb and the growing affordability gap as the market enters the busy spring home shopping season.

Zillow surveyed 20 metros and among current renters, homeownership aspirations were particularly strong, with about 10% of all renters nationwide saying they would like to buy within the next 12 months. In all but one of the 20 metros, more than 5% of all residents indicated they wanted to buy a home in the next year.

“For the housing market to continue its recovery, it is critical that homes are both available and remain affordable to meet the strong demand these survey results are predicting, particularly from first-time homebuyers,” said Zillow Chief Economist Stan Humphries. “Even after a wrenching housing recession, this data shows that the dream of homeownership remains very much alive and well, even in those areas that were hardest hit.

“But these aspirations must also contend with the current reality, and in many areas, conditions remain difficult for buyers. The market is moving toward more balance between buyers and sellers, but it is a slow and uneven process,” he said.

Most surveyed said they were confident or somewhat confident they could afford homeownership now, and if all renters who said they wanted to buy actually did purchase a home, it would represent more than 4.2 million first-time home sales.

That alone would be more than double the roughly 2.1 million first-time homebuyers in 2013.

Homeownership aspirations among current renters were the highest in Miami, Atlanta and Las Vegas, three metro areas that were among the hardest-hit by the housing recession, according to the Zillow homeownership aspirations index.

Market conditions remain mixed, though – inventory is up 11.1% nationally compared to a year ago, but it remains well below optimal levels, and has fallen year-over-year in eight of the 20 metro areas surveyed.

“Several of these drivers of overall housing confidence registered negative or only marginally positive readings in some cities,” said Pulsenomics founder Terry Loebs. “These data confirm that real estate recovery and economic healing are relative, local phenomena, and in some instances, likely reflect the lingering psychological impact of the housing bust.”

Recent data from the Census Bureau also indicates that builders are currently building more multifamily rental housing, rather than the entry-level homes today’s renters will likely be looking to buy in coming months.

Mortgage interest rates are also starting to creep upwards, standing at about 4.2% nationally, well above 2013 lows of roughly 3.3%.

Houses in several particularly hot markets, including San Francisco and through parts of Southern California, are becoming more unaffordable for buyers with lower incomes, especially first-time buyers.