WASHINGTON (Reuters) - President Barack Obama accused Republicans on Saturday of a backward approach to education funding that would mean further teacher layoffs, in a veiled swipe at Republican vice presidential hopeful Paul Ryan, who has led a drive for domestic-spending cuts.

Obama used his weekly radio and Internet address to press for increased investment in schools, as a new White House report showed more than 300,000 education jobs have been lost since the 2007-2009 recession and asserted that Republican budget proposals would call for cutting tens of thousands more.

Though Obama did not mention Ryan by name, the Wisconsin congressman - a fiscal hawk picked last week by Republican presidential candidate Mitt Romney to be his running mate - authored the Republicans' budget blueprint that passed the House of Representatives last March with no Democratic support.

The Ryan plan subsequently died in the Democratic-controlled Senate, but Obama's campaign wants voters to identify Romney with Ryan's austerity plan, especially with its potential impact on popular programs like Medicare and public education.

"This year, several thousand fewer educators will be going back to school," Obama said. "Since 2009, we've lost more than 300,000 education jobs, in part, because of budget cuts at the state and local level."

"At a time when the rest of the world is racing to out-educate America, these cuts force our kids into crowded classrooms," he said.

Obama earlier this year proposed $25 billion in funding for states to prevent teacher layoffs. But Republicans blocked the initiative because it was part of Obama's broader jobs package that they considered mostly wasteful spending.

"The economic plan that almost every Republican in Congress voted for would make the situation even worse. It would actually cut funding for education," he said. "All to pay for a massive new tax cut for millionaires and billionaires."

"That's backwards. That's wrong," he said.

Obama has focused on education as part of his strategy to paint himself as a champion of the middle class and cast Romney as out-of-touch with ordinary Americans.

The plan crafted by Ryan, chairman of the House budget committee, calls for reductions of about 20 percent in non-defense discretionary spending.

If these cuts were distributed evenly across budget areas, the White House report said, it would mean reductions in federal grants that would eliminate funding for 38,000 teachers and aides and a further 27,000 special-education teachers.

Ryan's budget plan attempts to slow the federal government's deficit spending, largely by cutting social programs and restructuring the Medicare healthcare system for the elderly. At the same time, Ryan proposed expensive income tax cuts, including rate reductions for the wealthy.

(Reporting By Matt Spetalnick; editing by Philip Barbara)