A tense vote on the Immigration Bill in the House of Commons this week saw plans to let the youngsters into Britain defeated by just 18 votes.
MPs cried shame as the Government scuppered a plan that would see the youngsters rescued from European refugee camps.
Home Secretary Theresa May had satisfied Tory rebels by agreeing to take 3,000 children from camps near Syria instead, but the move was defeated in the House of Lords.
And Conservative sources say the Government is planning a U-Turn.
One Tory source told the Sunday Mirror: “They are definitely willing to come to the table to avoid any potential problems.
“There’s no way they want to do this before the local elections .
“They don’t want to look weak and they are worried it might do damage in areas where immigration is an important issue.”
After the amendment was defeated the Immigration Bill went on to the House of Lords, and on Tuesday night, peers voted in favour of a compromise.
Lord Alf Dubs said it was Britain’s duty to ‘take our share’ of the children.
He added: “These are children who are vulnerable, children who are in danger, possibly fleeing for their lives.
“They’re liable to be lured into trafficking, possibly into prostitution.
“None of us would want our children to be in that environment.”
He added the Tory rejection left him “very upset” and he had “bent over backwards” to find a compromise the Government would accept.
After its defeat in the Lords the business returns to the House of Commons next Monday.
Conservative sources say the 18 vote margin of victory is not enough and leaves the Government vulnerable.
Reports say the Democratic Unionist Party, which traditionally votes with the government, is planning to lend its support to the Dubs Amendement, and although five Tories rebelled last time, a further 35 abstained.
Dr Tania Mathias said: “A lot of people were coming up to me after the debate telling me how they felt.
“No-one was critical. They were very supportive and were telling me they understood my position.
“I’m not sure what the numbers would be like if it came to another vote.”
Heidi Allen MP said: “I abstained during the last vote for two reasons.
“First, because I thought the Government had done a good job with the offer of taking 3,000 children from the region and I didn’t want to throw that back in their face.
“And I looked at the numbers and realised there weren’t enough of my side supporting, so I chose to abstain to keep the lines of communication open.
“But this time I will definitely vote for the amendment.
“This is the last chance to make a difference on it and whatever form it comes back in I’ll vote for it.”