The Democratic president has called for keeping the George W. Bush-era tax cuts in place for people earning under $250,000 a year but letting them expire for the wealthiest Americans.
But Ryan, the Wisconsin congressman who is the Republican nominee for vice president, said in his weekly podcast that Obama raised taxes 21 times in his first term and, if re-elected, "he'll raise taxes even more and our small businesses and middle-income families will suffer."
"President Obama refuses to get serious about spending," Ryan said. "And given the president's preference to raise taxes, just to pay the interest on the debt that the president has racked up and proposed, a middle-income family will see their tax bill grow by $4,000 a year."
Ryan said he and GOP presidential nominee Mitt Romney, if elected, would "get our spending under control."
"We'll put our budget on the track for balance. We'll cut our deficit. And we'll keep taxes low," he said.
He said Obama wants to "raise taxes by $2 trillion." He reiterated Romney's proposal for a "permanent, across-the-board, 20 percent cut in marginal tax rates."
"Then we'll eliminate current rates on interest, dividends and capital gains for anyone making less than $200,000 a year," Ryan said. "We will eliminate the alternative minimum tax and the death tax. And we will reform the tax code to make it simpler, fairer and more competitive."
He said doing that would bring the economy "roaring back to life."
"President Obama's tax plan will kill 700,000 jobs. Our tax plan will create 7 million new jobs -- and provide the kind of tax relief that our middle-income families and small businesses need," he said.