In the Commons, Nick Clegg explained how the study was needed to find out whether tenants could opt to take a smaller house or flat to avoid a reduction in their benefits. Under the reforms, tenants with one spare bedroom have had a payment cut of 14% and those deemed to have two or more spare have seen their benefits fall by 25%.
For special cases, councils have been handed a discretionary housing fund to help tenants pay their rent.
But Harriet Harman, Labour's deputy leader, who branded the tax "cruel and unfair", urged the Deputy Prime Minister to scrap it, saying: "What you don't want to admit, obviously, is that for 96% of tenants there isn't a smaller home to go to and so it is no wonder that the councils are saying that the discretionary housing fund on that basis is completely inadequate to help all the families who can't move and are falling into arrears."
Mr Clegg, pointing out how he suspected the problem "varied enormously" across the UK, explained how research was now under way to determine the impact of what the Government calls the single room subsidy.
"Of course, I accept that there will be cases where for some households this change from one system to another creates real dilemmas which need to be addressed through the money we are making available to local authorities," said the Deputy Prime Minister, stressing how the Coalition was now providing "hard cash for hard cases".
But one senior LibDem source made clear that, while the increasing welfare bill had to be cut, the way the policy was being implemented was building up a great deal of public and political resentment.
He suggested that a better way would have been to have a more thoughtful policy with greater explanation, more financial help and a longer transition period.
"These are people's homes after all, which some have lived in for 10, 20, 30 years.
"Once people start to get evicted, then the political situation will change," he warned.
It is thought that ahead of the General Election, there will be strong moves within the LibDem hierarchy to adopt a more qualified position on the bedroom tax going into the 2015 poll.
At the LibDem conference in Glasgow last month, many activists were angry at the party's support for the bedroom tax.
Activist Linda Jack, from Mid Bedfordshire, claimed the party seemed to have abandoned its values.
She said that she left the conference hall after the debate on the economy "wondering if there was still a place for me in this party".
Elsewhere, the latest TNS BMRB poll showed that the Tories enjoyed a post-conference boost with their level of support up five points and Labour's down three, giving Ed Miliband's party a mere two point lead at 36% to 34%.
UKIP were placed on 13% while the LibDems remained on 9%.