"I'm confident that we'll do it at least by Tuesday. We have a logistical challenge of getting everyone in town," he said on NBC.
Transport problems are persisting following a snowstorm that affected travel in the southeastern United States.
The US entered what is expected to be a brief shutdown on Saturday after Congress failed to approve a deal to keep a wide swath of operations funded.
The Senate easily passed a spending package on Friday but the House of Representatives is out of town.
Republican and Democratic lawmakers have been working to ensure a debate over immigration enforcement does not disrupt other government operations.
That is a contrast from the northern hemisphere autumn when both parties dug into their positions in a dispute over healthcare, prompting a shutdown that lasted a record 43 days and cost the US economy an estimated $US11 billion ($A16 billion).
The deal approved by the Senate would separate the Department of Homeland Security from the broader spending package.
This would allow lawmakers to approve funding for agencies such as the Pentagon and the Department of Labor while new restrictions are considered on federal immigration agents amid uproar after two US citizens were shot dead in Minneapolis.
Johnson, whose Republicans have a razor-thin majority in the House, said "our intention" is to fund all agencies except for DHS by Tuesday "and then we will have two weeks of good faith negotiations to figure it out".
The bill contains a two-week stop-gap measure to fund DHS but legislation on full-year DHS funding is in abeyance pending a deal on changes to ICE practices.
Democrats are demanding reforms for ICE such as requiring mandatory body cameras and ending their roving patrols and use of face masks.
"I just don't see how, in good conscience, Democrats can vote for continuing ICE funding when they're killing American citizens," Representative Ro Khanna, a California Democrat, told NBC.
Johnson said he believes US President Donald Trump's administration will make changes to some DHS practices but said ICE agents wear masks to protect their own identities and their families.
