Speaking to a conference of business leaders, the pro-EU Miliband said leaving Europe would be bad for prosperity and a betrayal of Britain's national interests.
"Increasingly we see euroscepticism on the rise among the British public - we see cabinet ministers in this government openly calling for Britain to leave," Miliband said.
"For those of us like me, who care passionately about our place in European Union, we cannot remain silent. I will not let Britain sleepwalk towards exit from the European Union."
Britain has long had an ambivalent relationship with the EU. The next general election is due in 2015.
Anti-EU lawmakers in Cameron's own Conservative party have urged him to take a hard line in the budget talks and resist EU demands for a real increase.
Cameron: 'The people of Europe are on my side'
Speaking to the same meeting earlier on Monday, Cameron said he felt he had the people of Europe on his side.
"I don't think it makes you a bad European because you want a tough budget settlement in Europe. I think it makes you a good European," he added.
"I feel I have got the people of Europe on my side in arguing that we should stop endlessly picking their pockets and spending more and more money through the EU budget, particularly when so many parts of the EU budget are not well spent."
Cameron has threatened to use his veto at the 22-23 November meeting to decide the EU's next seven-year budget to stop any agreement that is not in the interests of British taxpayers.
His spokeswoman said earlier on Monday that Britain believes a deal can be reached.
"The prime minister believes we can work through these details to get the right deal at this week's summit and we're ready to do that," the spokeswoman said, adding that Cameron had been "hitting the phones" speaking to other EU leaders.