ATLANTA — President Obama’s plan to expand preschool for the nation’s children faces deep skepticism among Republicans, who fear the creation of another federal entitlement program that they say could add to the nation’s deficit and swell the ranks of the teachers’ unions.

In a rally with teachers after visiting a class of 4-year-olds on Thursday, Mr. Obama reiterated his State of the Union pledge to make high-quality preschool available to all children, which could cost as much as $10 billion a year, or nearly a tenth of the entire federal education budget.

“Hope is found in what works,” Mr. Obama said to raucous applause after joining the children as they played with blocks and a magnifying glass. “This works. We know it works. If you are looking for a good bang for your educational buck, this is it. Right here.”

Despite the outlines of a plan that White House officials said would use federal money in support of state-based preschool programs, conservatives said they were suspicious that it would be a foot in the door toward more big government. They also said there was little evidence that large-scale preschool programs do much good for children in the long run. Advocates, who said that quality preschool education makes a significant difference in children’s lives, were bracing for a fight in Congress.