Work and Pensions Secretary Iain Duncan Smith said Labour - which is opposing the cap - was "in denial" over the state of the economy.
But Labour argued the cap would be a "hit and run" on working families.
Benefits have historically risen in line with the rate of inflation. The Commons vote is due at 19:00 GMT.
The House of Commons is debating the Welfare Benefits Uprating Bill, which would keep benefit rises to 1% for three years from next April.
The coalition argues this is necessary to reduce the deficit, and is fair at a time when public sector pay is being capped and salaries in the private sector are rising below the rate of inflation.
But Labour, which opposes the cap, says it will result in a real-terms cut in support for millions of working people.
Some Lib Dem MPs, including David Ward, John Leech, Julian Huppert and former minister Sarah Teather, are expected to rebel against the government while others - including Julian Huppert - could abstain.
Mr Leech, MP for Manchester Withington, said he found it "objectionable that the Tories are using 'skivers versus strivers' rhetoric to justify a cut to seven million working families".
Despite the concerns of some Lib Dems, the coalition is thought likely to win the vote.
Legislation is needed to implement changes announced by Chancellor George Osborne in last month's Autumn Statement - to cap increases in jobseeker's allowance, employment and support allowance, income support and elements of housing benefit.
The cap would also apply to maternity allowance, sick pay, maternity pay and paternity pay as well as the couple and lone parent elements of the working tax credit and the child element of the child tax credit.
These benefits traditionally rise in line with consumer prices in an annual process known as "uprating".
By Ross HawkinsPolitical correspondent, BBC News
Glance at the spreadsheets and the scale of the saving is apparent.
Figures in the Autumn Statement show raising many benefits and tax credits by 1% a year will save £2.8bn in 2015/16, compared with the government's previous plans.
The overall welfare budget in 2011/12, as calculated by the Institute for Fiscal Studies, is £201bn.
The political debate will centre on who should feel the pain.
Jobseekers Allowance totals 2.4% of the total bill, according to the IFS. Benefits for those on low incomes make up just under 21%.
Those for elderly people, including the state pension, make up over 42%.
The estimated value of fraud and error overpayments in benefit expenditure in 2011-12 is £3.2 billion.
They increased 5.2% this year and without the planned change would have been set to rise by 2.2% - the rate of CPI inflation last September, on which the figure is calculated. The rate of inflation has since risen to 2.7%.
During lively scenes in Parliament, Mr Duncan Smith said: "The number one priority now is reducing the deficit that they [Labour] left us - the biggest deficit since the Second World War."
He added that the gap between the rate of income inflation between workers and the unemployed had "grown" in the last few years.
"These are decisions that we are not taking easily but these are circumstances that they [Labour] are in denial about," Mr Duncan Smith said.
For Labour, shadow work and pensions secretary Liam Byrne accused the government of presiding over an increase in unemployment.
But Mr Duncan Smith said this was not the case and that the US and other European countries were faring worse than the UK.
Mr Byrne said the government was showing "contempt" by trying to "ram this bill through the House in just one day".
He added: "It's turning into a hit-and-run on working families and we should not stand for it."
Green Party MP Caroline Lucas said: "Isn't the truth of this that it's a mean and miserable piece of legislation from a mean and miserable government?"
Sarah Teather, who was replaced as an education minister in last autumn's government reshuffle, said she would oppose the bill "with a heavy heart" because it was "disingenuous" to try to "find someone to blame for our own woes".
"A fissure already exists between the working and non-working poor," she told MPs. "Hammering on that fault line with the language of 'shirkers and strivers' will have long-term impacts on public attitudes, on attitudes of one neighbour against another.
"It will make society less generous, less sympathetic, less able to co-operate."
However, Lib Dem deputy leader Simon Hughes told the House: "It's difficult but the government has got the right and I believe, after this parliament, it will be vindicated by getting more people in work and fewer out of work."
David Cameron's official spokesman said: "The prime minister's view is that the welfare system has to be brought back under control. The measures that the government has been taking, ever since the government came to power, have been designed to that end."
The BBC's political correspondent Gary O'Donoghue said an "impact assessment" published by the government suggested single parents would be most affected by the cap - losing £5 a week or about £250 over the three year period.
The majority of working age households in receipt of state support are likely be an average of £3 a week worse off.
The government has urged MPs to back a 1% cap on annual rises in working-age benefits and some tax credits, arguing it is vital to cutting the deficit.