Washington (CNN) Senate Majority Leader Mitch McConnell teed up a pivotal immigration debate for consideration next week early Friday morning, keeping a promise as soon as the Senate voted to end a government shutdown.

The move to hold an unpredictable Senate debate next week fulfills the promise McConnell made on the Senate floor to end the last government shutdown in mid-January, when he pledged to hold a neutral debate on the immigration issue that was "fair to all sides."

McConnell moved on the Senate floor to vote to open debate on the bill Monday evening. The bill McConnell chose was unrelated to immigration, after he had said he planned to use a separate bill for the debate.

That now sets up a chance for both sides to offer amendments that will compete for 60 votes -- the threshold to advance legislation in the Senate. If a proposal can garner 60 votes, it will pass the Senate but face an uncertain fate in the future.

The move still depends on the House, though, which first needs to vote to pass the budget deal negotiated in the Senate and fund the government. The bill was expected to pass, but vote counts remained unclear Friday morning. The House was set to vote in the early morning hours.

Read More