DUP MP Sammy Wilson has insiste the party is not in talks with Labour over a potential no-confidence vote in the House of Commons.
Jeremy Corbyn's Labour Party is reportedly considering a motion of no confidence in the Conservative government, which could ultimately force a general election.
But Mr Wilson told BBC Radio 5 Live's Emma Barnett: "We don't need to be in talks with Labour. We have made it quite clear that if the prime minister continues to pursue the policy and gets the ability to implement that policy, then we will vote against the government in a vote of no confidence.
"However, she has got to get over the first hurdle, and that is to get this agreement accepted by parliament. I don't believe she is ever going to get over that hurdle."
Mr Wilson said he did not expect progress on Theresa May's Withdrawal Agreement before the end of the year: "I don't think it's likely at all, because I suspect she's not even going to bring the deal back before Christmas, so she'll not be able to progress on this deal."
The Labour Party would put forward a motion of no confidence in Mrs May's government when it looked likely to succeed, a spokesman said.
The spokesman also told reporters it was clear Mrs May would not be able to achieve any substantial change to the divorce deal she has agreed with the European Union and he was confident it would fail to win the support of parliament.