In an interview marking five years as first minister, Carwyn Jones said people accepted Welsh ministers were not "miracle workers" on NHS matters.
He said Labour had "kept our promises" on health and other issues.
But a Conservative spokesman said the "greatest threat" to Welsh public services was an Ed Miliband government.
Discussing austerity, Mr Jones told BBC Wales: "If we see the Tory plans, we are going to have this until 2020.
"I do not know what the NHS in Wales would look like by 2020, or the education services, if we see those levels of cuts.
"We are just not going to be able to do what we all want to do, so I hope things will change or at least there will be hope in 2015."
In relation to problems in the NHS, he said: "If you are straight with people and say 'look there are problems in some parts of the NHS, money is not there as it was five or six years ago', they accept that.
"They know you are not miracle workers.
"But what you say to people is, we have prioritised those areas we think are important and also, of course, we have kept our promises on health and other areas," Mr Jones added.
A Welsh Conservative spokesman responded: "The greatest threat to Welsh public services is an Ed Miliband government increasing spending and borrowing, leading to crippling interest payments on the national debt, which would significantly reduce the money available to invest in schools and hospitals."
It is not known what the state of the NHS or education in Wales will be 2020 if the Conservatives win the general election, the first minister said.