Labour is facing pressure from its own members and voters for a referendum on the proposed European constitution, a senior Labour MP says.
Many Labour MPs are not happy with the EU constitution, says Mr Field
Former cabinet minister Frank Field says the issue could roll over into Labour's general election campaign.
His comments follow Tory calls to voters to use the European elections in June to voice their views on what the party calls "this dangerous document".
Tony Blair has said he wants an early deal on the draft treaty.
The re-drafting of the constitution has been prompted by the EU's forthcoming expansion, and the deadline date for European ministers to wrap up the debate is 17 June.
But Mr Field told the BBC the government was facing "a huge amount of dispute ahead of them" over the matter.
Many issues had still to be dealt with in this "crucial period", he said.
"We have a government trying to push this issue through parliament," he said, adding that at least 30 Labour members were "deeply troubled" and wanted a referendum.
Getting the vote in parliament could backfire due to the strength of feeling among voters, he said.
"I think the feelings will be so great in the country that even if the government is successful in using its majority to that effect, it is an issue which will roll over into the general election campaign and this is not an issue on which Labour wins votes."
'Prepared to be overruled'
He said he supported calls for a referendum, although not at the same time as the European elections.
Such a referendum would display "a new alliance with the voters", he said.
Even if this meant losing, he said this would show a government "prepared to accept being overruled and actually taking voters' views on board".
Earlier shadow foreign secretary Michael Ancram said voters should use the 10 June European elections to show how strongly they felt about a constitution.
He told BBC Radio 4's Today programme: "People who feel strongly that this constitution is dangerous for this country, which I believe and my party believe it is, will be able to show that
by voting in these elections."
But he stressed that the elections could not be a substitute for a referendum, but could be used as a means of voicing opinion.
"There are many people who are angry
because they see they are being denied their right to have a say on this very important issue."
The prime minister said he was not prepared to give away British controls on key policies like tax, defence and criminal justice, after the summit closed on Friday.
Former Tory deputy prime minister Lord Heseltine, speaking on the Today programme on Saturday, stood firmly against his leader's call for a referendum and supported the signing of the constitution by the UK.
"I believe Britain gains from involvement in Europe," he said.
"The more we can share power in the agreed fields, the more we can influence to our advantage the way Europe develops."
He said the "Euro-sceptic press in the UK" was influencing voters.
Mr Blair says a constitution is necessary when 10 new members join on 1 May expanding the EU to 25 members.
But critics say a constitution is a step towards a federal Europe and the loss of British sovereignty.