The Chancellor said the Conservatives were "not deaf" to the message that had been delivered at the ballot box on June 8 and would be looking at the plans it had for cuts to winter fuel allowances and ending the triple lock on pensions.
But Mr Hammond left the door open to raising taxes and said borrowing more is "not the solution".
"I think people are weary of the long slog," he told BBC One's Andrew Marr Show.
Asked if he would go ahead with £3 billion of cuts to local government, he replied: "We've set out a series of measures that are already legislated for. We have other proposals that we will now have to look at again in the light of the General Election result and in the new parliament.
"I will be delivering a budget in the autumn and you will find out then what we are proposing.
"There's not going to be a summer budget or anything like that."
Pressed on whether the government would have to change direction, particularly if it does a deal with the DUP which is opposed to cuts to the winter fuel allowance and the end of the triple lock on pensions, he replied: "We will look at all these things. Obviously we are not deaf. We heard a message last week in the General Election and we need to look at how we deal with the challenges we face in the economy.
"I understand that people are weary after years of hard work to rebuild the economy after the great crash of 2008-09, but we have to live within our means.
"More borrowing, which seems to be Jeremy Corbyn's answer, is not the solution.
"We have never said we won't raise some taxes. Overall, we are a government that believes in low taxes and we want to reduce the burden of taxes overall for working families."
Mr Hammond said Brexit meant the UK would definitely be leaving the single market, but must avoid "cliff edges".
"What we put in place may not be a single arrangement that endures for ever, it may be an arrangement which lasts for a couple of years as a temporary measure before we get to the long-term agreed status quo," he told Marr.
"We're leaving the EU and because we are leaving the EU, we will be leaving the single market and by the way, we will be leaving the customs union.
"The question is not whether we are leaving the customs union. The question is what do we put in its place in order to deliver the objectives the Prime Minister set out in her Lancaster House speech of having no hard land border in Ireland and enabling British goods to flow freely backwards and forwards across the border with the European Union?
"It's a statement of common sense that if we are going to radically change the way we work together, we need to get there via a slope, not a cliff edge."
Mr Hammond said he would not agree to a deal that would "destroy" Britain.
"No deal would be a very, very bad outcome for Britain, but there is a possible worse outcome and that is a deal that is deliberately structured to suck the lifeblood out of our economy over a period of time."
Commons leader Andrea Leadsom, a leading Brexit supporter, said she believed the two-year timetable could be met.
She told BBC One's Sunday Politics: "Where you have politicians right across the EU and the United Kingdom who share the desire for a successful outcome, with low tariffs, zero non-tariff barriers, free trade between ourselves, cooperation on security and so on, it should be perfectly possible to meet the time frame.
Asked if that meant no transitional arrangements, she replied: "Well, I'm extremely optimistic that we will find there is a lot we can agree on."