The reasons: Limited supply of homes, soaring prices and strict lending standards.

"The dream of homeownership remains very much alive and well," said Zillow's chief economist Stan Humphries. "But these aspirations must also contend with the current reality, and in many areas, conditions remain difficult."

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In all but one of 20 metro areas Zillow surveyed, 5% or more of residents said they wanted to buy a home over the next 12 months. The desire is particularly strong for renters: 10% of them want to buy. That would translate into 4.2 million first-time buyers, double the number who purchased in 2013.