Dozens of Conservatives were expected to defy the government and oppose the plan to limit the time available for debating plans for proposed changes.
But the government later won a separate vote on the principle behind a mainly elected chamber with a majority of 338.
But 91 Conservative MPs voted against the bill as a whole.
One of the rebels, Angie Bray, has been sacked from her role as a ministerial aide.
The vote means that proposals for an 80% elected House of Lords that is half its current size will proceed to their next stage of parliamentary scrutiny in the autumn.
By Robin BrantPolitical Correspondent, BBC News
Nick Clegg's dream of reform of the House of Lords has slipped away.
Not forever, not yet anyway, but it's suffered a very significant setback.
The reason: David Cameron couldn't deliver the numbers.
And it is, ultimately, a numbers game.
The prime minister was facing a massive rebellion, so he decided to step back, apparently telling his deputy he needed more time to garner support from the Tory side.
So the government has opted for another go in the autumn, when it says it will try, again, to get support for a programme motion.
On the face of it it weakens both men. One couldn't persuade a sizeable chunk of his own MPs to back a key part of the coalition's policy programme.
The other has failed the first test in delivering what he hoped would be a key legacy of his time in office.
The more Machiavellian view is of a prime minister who sanctioned a soft whipping operation and who wanted to see the prospect of an insurrection in the 100+ category.
And also of a man who is content to present his coalition partner with the harsh reality of another delay on the road to reforming the Lords.
But critics said the whole future of the bill has been thrown into doubt by the government's decision not to put a so-called programme motion to a vote. This would have limited the time for future debate on the proposed changes in the House of Commons to 10 days.
The government had been facing defeat on the vote and Lib Dem sources say Prime Minister David Cameron told his deputy Nick Clegg that the timetabling motion should be pulled to gather support for it among Conservatives over the next two months.
BBC political editor Nick Robinson said a spokesman for Mr Clegg had declared "a plague on both their houses" when asked whether he blamed the Conservatives or Labour for the setback.
Labour and rebel Conservative MPs said this did not allow enough time to discuss a crucial constitutional change.
Commons leader Sir George Young told MPs the timetabling vote would be postponed until after the summer recess.
He blamed Labour for the climbdown, saying the opposition was not prepared to support the government in Tuesday's vote despite supporting the idea of changes to the Lords. "It needs those that support reform to vote for reform," he said.
The government "remain committed to making progress" on changing the composition of the Lords, he stressed.
Responding to the setback, Foreign Secretary William Hague said all parties must "try to establish a better consensus", while former Lib Dem minister David Laws said it was "frustrating" but the government would return to the issue in two months and "expect to win".
But Tory MP Conor Burns resigned from his position as a ministerial aide in the Northern Ireland Office in protest at the plans.
And Tory backbencher Jesse Norman said the government had backed down because of the scale of the likely rebellion on the Conservative benches and the proposals were now a "dead duck".
And Bernard Jenkin, one of the leading Conservative opponents of the plans, questioned the future of the entire legislation.
"Whatever moral authority the bill had, it has now lost," he said.
Labour described the decision not to press ahead with a vote on the issue of the time allocated for debate as a "victory for Parliament".
"This is not a wrecking tactic - far from it," said shadow justice secretary Sadiq Khan. "We've already given our assurances we'll do all we can to ensure the bill progresses. Instead, it's about making good an inadequate bill.
"And that means allowing Parliament the time to revise, amend and improve the bill free from the threat of debate being stifled."
Commons Speaker John Bercow has told MPs that the parliamentary rules mean that even if - as expected - the bill is given a second reading it will not move on to the next stage of the parliamentary process.
Before it can be considered again, MPs will first need to vote for a committal motion that will formally send the bill into committee.
The coalition has dropped plans for a crucial vote on its plans to reform the House of Lords after it faced likely defeat over the issue.