The rule was supported by every voting Republican, and opposed by every voting Democrat.
"The majority has made clear that their vision for America is a vision that says the nation can no longer care for our seniors, that we must halt vital scientific research, and that we should let our bridges and schools crumble because we cannot afford to invest in the future," Rep. Louise Slaughter (D-N.Y.) said.
"In short, I believe it is an extremely cynical vision for America, and one that I strongly reject."
Republicans replied that Ryan's budget allows for increased spending over the next 10 years, but at a slower rate, which allows for $5.7 trillion in deficit reduction over that decade.
"I promised myself I would count how many times we heard the words 'extreme cuts' applied to what is a half trillion dollars in new and additional spending, but I confess I've lost track already today," Rep. Rob Woodall (R-Ga.) said.
Woodall said the GOP budget would balance in 10 years and lower taxes, and criticized Democrats for failing to provide a pathway to balance. He also criticized President Obama for saying his budget would come out long after the House considers budget options this week.
"I think it is fair that we ask in this debate why we have been denied a chance to look at the president's budget," he said.
In addition to the Ryan budget, the rule allows for debate and votes on five other options. The Republican Study Committee's budget proposal most aggressively limits spending, followed by Ryan's budget, the mainstream Democratic budget, and budgets from the Congressional Black Caucus and the Progressive Caucus.
The rule for the budget also allows consideration of a resolution setting funding levels for House committees in the 113th Congress. Woodall said House Republicans have cut committee spending from $300 million in the 111th Congress, to $260 million in the 112th, to $240 million in the 113th.
"Thrift begins at home," he said. The House was expected to debate and vote on the committee spending resolution immediately after the rule vote, then hold some general debate on the Ryan budget Tuesday evening.