The Ohio congressman had hoped to demonstrate Republican unity by passing a bill through the House, known as "Plan B," that would limit income-tax increases to the wealthiest sliver of the population - those earning $1 million and more, a far smaller slice of taxpayers than Obama wants to pay higher taxes.
But Boehner canceled the vote after failing to round up enough support from his party because many conservative Republicans are opposed to tax hikes on even the richest wage-earning Americans.
"The House did not take up the tax measure today because it did not have sufficient support from our members to pass," Boehner said in a statement after huddling with other Republican leaders.
The White House pledged to work with Congress to reach a deal as quickly as possible.
"We are hopeful that we will be able to find a bipartisan solution quickly that protects the middle class and our economy," White House spokesman Jay Carney said in a statement.
The bill, had it passed, would have put Republicans on record as supporting a tax increase on those who earn more than $1 million per year, breaking with decades of orthodoxy. It won the blessing of influential anti-tax activist Grover Norquist, but other conservative groups fiercely opposed it and many rank-and-file members said they would not support it.
Obama wants to raise taxes on families earning more than $400,000, a much lower threshold.