Democratic Unionist Party sources have urged the Conservatives to give a “greater focus” to their negotiations.
A senior DUP source said the party could not be “taken for granted” – adding that if the PM could not reach a deal, “what does that mean for bigger negotiations she is involved in?”
No deal has been reached after 10 days of talks between the parties.
But sources told the BBC’s Laura Kuenssberg they believed a deal would still be done.
The Conservatives are hoping the DUP will sustain their minority government.
The warning from a senior DUP source to BBC Northern Ireland political editor Mark Devenport comes the day before the government’s Queen’s Speech is presented to Parliament.
Although they have not reached a final deal, DUP leader Arlene Foster has said it is “right and proper” that her MPs support the Conservative government’s first Queen’s Speech.
A Conservative source said it was important the party “gets on with its business” as talks continue by putting forward Wednesday’s Queen’s Speech.
Earlier cabinet minister Chris Grayling predicted a “sensible” deal would be reached.
The transport secretary said the talks were “going well”, adding that the DUP, which has 10 MPs, did not want another election or Jeremy Corbyn in Downing Street.
Theresa May is seeking to negotiate a so-called “confidence and supply” arrangement whereby the DUP will throw their weight behind the government in key Commons votes, such as on the Queen’s Speech and Budgets.
It is a week since DUP leader Arlene Foster visited Downing Street for talks with Theresa May, with reports that a final agreement is being held up by discussions over extra funding for Northern Ireland.
Should Mrs May lose any votes on the Queen’s Speech, which are expected to take place next week, it would amount to a vote of no confidence in the government and put its future in doubt.
But Mr Grayling told BBC Radio 4’s Today programme that he did not expect this to happen.
“The talks are going on but one thing I am absolutely certain of is that the DUP do not want to see another election and Jeremy Corbyn in Downing Street,” he said. “We are having good, constructive discussions and I am confident we will reach a sensible agreement.”
Former Prime Minister Sir John Major has urged Theresa May to reconsider her approach, saying a deal with the DUP could threaten the Northern Ireland peace process and “carry baggage” for his party. He has said the Conservatives should be able to govern anyway with the DUP’s tacit support.
Asked about the repercussions if there was no agreement, Mr Grayling replied: “I am not pessimistic about this. I think we will have a sensible arrangement.
“We have got some days until we have a vote on the Queen’s Speech. It is not on Queen’s Speech day. The vote happens many days later as we have an extended debate first and I am sure we will have a sensible arrangement between the parties when that time comes.”
The DUP had made it clear, he added, that they did not want “an unstable government undermining our union” and wanted to see us “go ahead with the Brexit negotiations with a sensible government in place”.