Andrew Marr suggested that it was "too late" for Labor Brexit plans as the country approaches the date of departure from the European Union.
Britain will officially leave the European Union on March 29, 2019, but the Prime Minister agreed to a transition period that will keep the United Kingdom paying the block until December 2020.
Speaking on Andrew Marr's show, the presenter said: "There is a real danger, we are running out of time." The end of March next year is quite close.
"From your point of view, starting the negotiation again with the idea of Labor, it's too late for that now, is not it? It's too late."
Sir Keir replied: "The logic of that argument is that you have to vote for anything that the Prime Minister brings back in. We do not accept that."
He added: "We do not accept this proposal, it is an agreement of Theresa May or no agreement, and it is not just us.
"There is a large majority in parliament that will not accept that the alternative to Theresa May's agreement, or if there is one, is not an agreement." That majority will speak when we get to this vote. "
During the BBC interview, the Labor Party leader was asked if Labor's plans for a customs union were feasible.
Sir Keir said: "Yes, I have discussed it throughout the EU." That idea would never have arisen if it had not had these discussions, not only in Brussels but in other EU countries.
"The idea of a customs union being made to work is something that people are very interested in and they would discuss it, it would be a million miles from where we are now."
Sir Keir added: "In the discussions I have had, I have made it clear that we are not looking for a Turkish-style solution; If that is all that is offered, then this would not be something that we want to negotiate. "
The Labor Brexit secretary also stated that even if Ms. May reaches an agreement with the European Union, the Tory MP will "break it next year".
He said: "I think we should ask ourselves the question if there is an agreement before Christmas that will last for a long time, this idea will be a solution, the problem will be over."
"I do not think anyone thinks that this 30-year civil war at the Tory party in Europe is going to end before Christmas.
"What we're going to see is that even if there's an agreement, the Tory party will try to break it next year, some are already saying they're going to do it, so this idea of a historic moment just before Christmas in the national interest It will not happen, they will not stop fighting over this.
"We have reached the grave situation in which people say," Is this government really capable of fulfilling it because it is so divided? "
Sir Keir repeated that the Labor Party would apply its six tests to any agreement that the Prime Minister brings from Brussels.
The host of the BBC, Marr, also asked Sir Keir about the progress of the popular vote after some 700,000 joined the protest in London to demand another Brexit vote.
Sir Keir replied: "It's a very significant number, I think the fact of the march, the size of the march is significant, but I think it reflects a much larger group, I think Leave and Remain, which is completely losing confidence. in the capacity of the Prime Minister to reach an agreement ".
The Labor Bank insisted that Labor's preference is a general election, but everyone the options remain "on the table" in the event that Ms. May's Brexit agreement is rejected in the House of Commons.