* May's government suggests it's open to compromise
* Opposition Labour still waiting for changes to "red lines"
* All agree time is running out for Brexit to be clinched
* Cause pain for EU if Britain stays in -senior eurosceptic
By Elizabeth Piper
LONDON, April 7 (Reuters) - Britain's government held out the possibility of compromise on Sunday with the opposition Labour Party to try to win support in parliament for leaving the European Union with a deal, just days before the latest Brexit date.
Prime Minister Theresa May, weaker than ever after her Brexit deal was rejected by parliament three times, has been forced to turn to Labour leader Jeremy Corbyn after giving up on winning over eurosceptics in her Conservative Party, whose opposition has hardened.
With Britain's departure now set for April 12, May's government is running out of time to get a deal through Britain's divided parliament, and must come up with a new plan to secure a new delay from EU leaders at a summit on Wednesday.
Britain's biggest shift in foreign and trade policy in more than 40 years is mired in uncertainty, with ministers saying Brexit may never happen, businesses worried the country could leave without a deal, and others just wanting to reverse it.
In a last-ditch bid to get her deal through parliament, May opened talks with Corbyn last week to try to strike a deal on Britain's future ties with the EU in exchange for his support for her divorce deal, the Withdrawal Agreement.
So far those talks have failed to yield any kind of accord, with Labour policy chiefs saying the government has yet to move from its "red lines", above all over a customs union, which sets tariffs for goods imported into the EU.
"Specifically provided we are leaving the European Union then it is important that we compromise, that's what this is about and it is through gritted teeth," said Andrea Leadsom, the Brexit-supporting leader of the House of Commons (lower house of parliament).
"But nevertheless the most important thing is to actually leave the EU," she told the BBC's Andrew Marr show, adding that May's proposal for a customs arrangement after Brexit was not too far from Labour's desire for a customs union.
But, while describing the talks so far as positive, Labour's business policy chief Rebecca Long-Bailey said there had as yet been no "real changes" to the deal.
"I think both sides are committed to working quite rigorously to compromise as much as possible so that we can provide that compromise Brexit deal that I think parliament desperately needs at the moment," she told the BBC.