Time is running out for the Trump administration to enact its agenda, and disagreements on key issues between the White House, the Senate and the House will make things even harder, former Republican leader Michael Steele told CNBC on Monday.

"The tension is already there on some big-ticket items like tax reform and health care that the Senate is of one mind, the House is of another and the White House is on a completely different page," the former chairman of the Republican National Committee said on "Squawk Box."

He said the debt ceiling represents the strains between the executive and legislative branches.

There are Republicans who came into Congress promising that they would not vote for any increase in the federal debt limit, Steele said. "But the president has already made it very clear he wants a clean vote, he wants a clean debt-spending bill increase on the table."

The nonpartisan Congressional Budget Office has estimated the government will hit its debt limit in mid-October and will need to raise its borrowing limit or risk defaulting on its debt obligations.

Steele said now is the time to pass things that are important to the administration like tax reform partly because of next year's elections. He said more pressing issues like the debt ceiling are likely to make tax reform difficult.

He said an added problem for congressional Republicans is former chief strategist Stephen Bannon, who departed the Trump White House on Friday and is planning to use his role at Breitbart News to "go after" those who have compromised the president's agenda.

"This fall is not going to be pretty for Republicans," he said.