Ryan also revived his proposal to reform Medicare, the health care program for senior citizens that is considered the biggest driver of rising federal deficits as costs increase and more Americans become eligible.
The idea was a major issue in last year's presidential election, in which Ryan was the vice presidential candidate on the GOP ticket that lost to Obama.
It calls for offering senior citizens a choice between traditional fee-for-service Medicare and a premium support system that would provide a fixed government payment to help them buy private health insurance. The plan would take effect in 2024 to exempt people 55 and older today.
Both sides reverted to harsh rhetoric from last year's election campaign in defending their deeply entrenched positions on Wednesday.
Ryan referred to "job-killing tax increases" pushed by Obama and Democrats, saying his push for less government and lower tax rates would benefit economic growth.
"What we're saying, like we said before, is we can hit these same revenue numbers without killing jobs," he contended, adding that budgets were all about priorities and choices.
Democrats responded that the Ryan proposal would harm economic growth by shifting the burden of deficit reduction to middle-class Americans, the elderly and others, while cutting spending for college loans, infrastructure development, scientific research and other areas vital for job creation.
"It is not consistent with American values. It is not fiscally responsible," argued Rep. Kathy Castor, D-Florida.
In the ABC interview, Obama took aim at the choices in Ryan's budget plan.
"If you look at what Paul Ryan does to balance the budget, it means that you have to 'voucherize' Medicare, you have to slash deeply into programs like Medicaid, you've essentially got to either tax middle-class families a lot higher than you currently are or you can't lower rates the way he's promised," the president said.
For his part, Ryan noted that while his side lost last year's election, his 2014 budget plan adhered to GOP principles that the party believes will set the country on the right path to growth and prosperity.
However, he sounded contradictory when challenged by reporters Tuesday about his call to eliminate most of Obama's health care reform law. After first saying "we are not going to re-fight the past" and that "law is law" with regard to the measure known as Obamacare, Ryan later said that "we need to repeal and replace Obamacare with a better system."
Republicans led by their conservative base seek to shrink the size and cost of government, opposing any new tax revenue while pushing for spending cuts and lower tax rates that they say will spur more economic growth.
After agreeing in January to allow tax rates on top income earners to return to higher levels of the 1990s, Republican leaders say they oppose any further steps to raise taxes.
Obama and Democrats say they want to protect Medicare, Medicaid and Social Security, and that comprehensive deficit reduction must include increased taxes on wealthy Americans to prevent the burden of austerity steps from shifting too much to the middle class, the elderly and other vulnerable demographics.
By clearly staking out positions in their budget proposals, Obama and Congress appear intent on trying to avoid the crisis-driven brinksmanship of the past four years.
However, the familiar, partisan nature of the budget plans illuminated the continuing political division that the public blames for legislative dysfunction.
A CBS News poll last week showed more than 70% of respondents want both sides to compromise to end the brinksmanship over taxes and spending that dominated Obama's first term.
During the past four years, House Republicans pushed through partisan budgets that Senate Democrats ignored, forcing the repeated extension of past spending plans.
Meanwhile, the president's budget proposals generated little support in Congress.
The upcoming negotiations are complicated by lingering fiscal issues from past showdowns.
Deep cuts to military and other discretionary spending took effect this month, and both sides were expected to try to soften their impact through a separate funding measure for the rest of the current fiscal year, which ends September 30.
Called a continuing resolution, it must pass by March 27 to prevent a partial government shutdown. The Republican-led House passed its version last week, and the Democrat-led Senate took up its own version this week.
Congress also must authorize an increase in the federal borrowing limit this summer, and Republicans have made clear they intend to leverage that moment to try to extract concessions.
A comprehensive deficit-reduction deal appeared close during Obama's first term, but eventually fell apart over taxes.