Negotiations over Britain's EU membership reforms remain "fragile", European Council president Donald Tusk said as he announced he was cancelling other engagements to try to ensure agreement at a summit next week.
Prime Minister David Cameron hopes to secure a final reform package when leaders from the 28-strong bloc meet in Brussels to allow the promised in/out referendum to be held before the summer.
Foreign Secretary Philip Hammond told MPs his own talks with counterparts at the weekend convinced him there was "the basis of a workable deal" on the most controversial issue of curbing migrant workers' benefits.
But there were fresh signs that the proposals - including an "emergency brake" on welfare payments - had failed to win public support, with a poll showing the numbers backing Brexit drawing level with those preferring to stay in.
Tory MP Steve Baker, chairman of Conservatives for Britain, claimed a member of the Government told him the pro-EU camp had "expected at this stage to be 20 to 30 points ahead".
"We have so slammed it that we, the leave side, are nine points ahead," he said of the most extreme of recent polls.
"Let's celebrate that we are winning."
In a statement Mr Tusk, who will chair the February 18/19 summit, said:"I am confident that this is a balanced and solid proposal and I hope to finalise it next week in the European Council.
"However, let me be clear, this is a very fragile political process. Therefore I have decided to cancel all my obligations and will hold a number of meetings with EU leaders and with the European Parliament in order to help reach an agreement."
French President Francois Hollande, German Chancellor Angela Merkel, Greek Prime Minister Alexis Tsipras, Romanian President Klaus Iohannis and Czech PM Bohuslav Sobotka are among those in his diary.
A survey by ICM found that the two sides of the argument were locked at 50% to 50% among voters who had made up their minds - a two-point rise for "leave" and a similar dip for "remain" since the proposals emerged last week.
Mr Hammond told the Commons European Scrutiny Committee that remaining obstacles could be overcome.
"I won't say everybody is delighted but, broadly, the mood was that those countries who could be expected to have been critical of this approach were impressed with the way the Council had managed to find a solution which addressed the UK's needs without trampling roughshod over their cherished principles," he said about the welfare provisions.
He also claimed that the EU as a whole was moving in a more Brussels-sceptical direction, saying he could think of nine member states that would "instinctively align with us" on key issues.
As campaigners on both sides stepped up efforts to win over voters, Liberal Democrat leader Tim Farron said that while the EU was not perfect, "picking up your ball in a sulk and heading home, is not the way to win".
He added: "We should be a leading voice to make changes. Remaining in a reformed Europe."
He accused Mr Cameron of engaging in "a nasty race to the bottom on immigration, migration and refugees" by refusing demands to take in more refugees from Europe - including 3,000 unaccompanied children.
And he called on Labour leader Jeremy Corbyn to "step up" with a strongly pro-EU Labour campaign.
MP Graham Brady, who chairs the influential Tory backbench 1922 Committee, said he expected around 100 colleagues to openly back Brexit - significantly higher than the 50-70 recently mooted by Mr Baker.
But he told the New Statesman magazine he was not among those who believed Mr Cameron should quit as Prime Minister if the country voted to leave the EU against his recommendation.
"When we vote to leave the European Union I think it is very important that we have a period of stability. I think it would be hugely valuable to have an experienced team in place to deal with the renegotiation.
"I think it's actually very important that the Prime Minister should stay."
He said he expected at least one of the candidates to replace Mr Cameron as party leader when he does step down would be someone who had campaigned for Brexit.