He acknowledged that more work was needed to get the United Kingdom ready for Brexit on March 29, telling the BBC's Andrew Marr Show there are "still steps that are currently being put in place" but "there is steady work that is going on, 10,000 civil servants that are now focused on this" and the Border Force was "ramping up" its staff.
With only 47 days to go, there have been claims the prime minister is running down the clock to make it more likely that MPs will back her withdrawal agreement as so many of them fear a no-deal departure. She is due to update parliament on her progress in talks with the European Union on Wednesday.
On Wednesday, Mrs May will ask MPs for more time to get legally-binding changes to the controversial Northern Irish backstop, which she believes will be enough to secure a majority in Parliament for her deal.
In the vote this week lawmakers are set to have their say on amendments that could limit May's options and give parliament a broader say over the Brexit process.
Speaking on the BBC's Andrew Marr Show on Sunday morning, Brokenshire said if a deal had not been agreed by February 27 then MPs would be allowed to again vote on their own proposals as to what should happen.
"That gives that sense of timetable, clarity, and goal on what we're doing with the European Union - taking that work forward and our determination to get a deal - but equally knowing that role that parliament very firmly has", Brokenshire told the BBC.
The British government is seeking to win more time to secure European Union concessions on Brexit that could pass parliament and avert a chaotic split from the bloc on March 29.
Britain's economic slowdown should not be blamed entirely on Brexit, British Trade Minister Liam Fox said on Monday after data showed the economy past year grew at its slowest since 2012.
But it was rejected by the UK Parliament and if it is not approved by Brexit day, the default position would be a no-deal Brexit.
The EU and the Irish Government have insisted that the backstop is the best way of guaranteeing there will be no hard border in Ireland.