DECATUR, Ga. — Raising hopes among parents who want preschool for all, President Barack Obama on Thursday rolled out a plan to vastly expand government-funded early childhood while keeping the price tag a secret.

Republicans, wary of high costs and questionable outcomes, made clear they have no intention of signing a blank check.

Setting up yet another clash with Republicans over spending and the proper scope of government, Obama in his State of the Union address proposed working with states to make high-quality preschool available to every American child. Two days later, he played blocks and gave fist-bumps to kids in a preschool classroom at the College Heights Early Childhood Learning Center in Decatur, casting the plan as part of a moral imperative to give every child a shot at success.

“The size of your paycheck shouldn’t determine your child’s future,” Obama told about 600 teachers and parents at the Decatur Community Recreation Center, singling out Georgia as a model for making universal preschool a priority. “Let’s fix this. Let’s make sure none of our kids start out the race of life already a step behind.”

The White House offered the first details about Obama’s plan Thursday, describing it as a “continuum of high-quality early learning for a child, beginning at birth and continuing to age 5.” The government would fund public preschool for any 4-year-old whose family income is 200 percent or less of the federal poverty level — a more generous threshold than the current Head Start program, which generally serves kids from families below 130 percent of the poverty line. All 50 states and the federal government would chip in.

Obama also proposed letting communities and child care providers compete for grants to serve children 3 and younger, starting from birth. And once a state has established its program for 4-year-olds, it can use funds from the program to offer full-day kindergarten, the plan says.

Conspicuously absent from Obama’s plan were any details about the cost, a key concern among Republicans. Obama’s aides have insisted the new programs would not add to the nation’s nearly $16.5 trillion debt, but they won’t say what else will be cut to offset the cost, offering only vague allusions to cutting entitlement spending and closing loopholes.

In a conference call with reporters Thursday, two of Obama’s top policy aides declined five times to explain how much the program would cost.

“Details on that will be released with the president releases his budget in the coming weeks,” said Roberto Rodriguez, the White House’s top education adviser. When asked again about the costs, officials went silent before a press aide joked: “Great, we’ll take the next one.”

The price tag for expanding preschool to more than 4 million 4-year-olds is potentially staggering. For instance, the Center for American Progress, a liberal think tank with close ties to the Obama administration, proposed a $10,000-a-child match to what states spend. That effort could cost tax payers almost $100 billion over 10 years.

Democrats and Republicans have already gridlocked over where to find $1.2 trillion in spending cuts over the next decade mandated by the so-called sequester; it’s difficult to imagine they could reach consensus on those cuts plus agree on further cuts to offset expanded preschool.

In fact, the sequester cuts themselves could devastate current pre-kindergarten programs, Education Secretary Arne Duncan said Thursday, if Congress doesn’t find a way out by March 1, the date the cuts kick in. “Doing that to our most vulnerable children is education malpractice, economically foolish and morally indefensible,” he told senators on Capitol Hill.

Weary of proposals by Obama they say blow up the cost and reach of federal government and still licking their wounds from November’s election, Republicans are in no rush to sign off on Obama’s preschool plan or any of a number of other initiatives he pitched in his address on Tuesday.

“That whole playing well with others, by the way, is a trait we could use more in Washington,” Obama said to a mix of laughter and applause in Decatur. “Maybe we need to bring the teachers up every once in a while have some quiet time. Time out.”

A day earlier, House Speaker John Boehner said involving the federal government in early childhood education was “a good way to screw it up,” a sentiment echoed by Rep. John Kline, who chairs the House panel on education and said Obama must answer basic questions before expecting Republicans to get on board.

“Will the plan be affordable? We all want to give children a solid foundation for a bright future, but that also means we can’t saddle them with even more debt,” Klein said.

Republican lawmakers also were eager to press Obama for specifics lacking in his speech. For instance, leaders on the Hill were curious if this new expansion would be part of existing programs such as Head Start in the Health and Human Services Department, or if it would start a new program inside the Education Department. They also wanted to know if the new effort would funnel money to states or local governments, or if Washington would administer the program as part of a national pre-K program that is unrivaled in size.

Obama has said he wants to partner with states, but the mechanics of such a joint project were far from clear. White House officials did say the new pre-kindergarten plans would be set up by states and independent of Washington’s meddling with the details.

Speaking broadly about its virtues, Obama said such an initiative would shrink the achievement gap for poor and minority students and strengthen a competitive workforce that would attract companies to create jobs in the U.S.

“This works. We know it works,” Obama said. “If you are looking for a good bang for your educational buck, this is it right here.”

Republicans and conservatives have questioned the effectiveness of Head Start programs, citing studies such as a Health and Human Services Department report last year showing that, while at-risk students enrolled in the pre-kindergarten programs saw tremendous gains in vocabulary and social development, those benefits largely faded by the time students reached third grade.

Scores of other studies, however, were more favorable toward the program, which has been shown to make at-risk students more likely to complete high school and avoid criminal arrests. In pure dollars and cents, academics called it a smart investment.

Even in states like Georgia, showcased by Obama in his remarks Thursday, the results have been mixed. Georgia made a commitment to universal pre-K in 1995 and it’s been a slow climb, with about 60 percent of eligible children currently enrolled. And Georgia’s high school graduation rate is among the lowest in the nation.