The Senate is poised to delay a House-passed disaster relief bill until January as lawmakers appear unable to reach a deal to speed up consideration of the legislation.

Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas), whose state was hit by Hurricane Harvey earlier this year, said lawmakers didn't "have enough time" to pass the bill with Congress expected to wrap up their work for the year on Thursday.

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"We have to go through the whole process absent unanimous consent. It would take us a week," he told reporters on Thursday.

He added, "I don't think we have enough time to vote on disaster aid."

The disaster relief bill passed the House in a 251-169 vote earlier Thursday after delegations from states impacted by a string of recent disasters demanded it be passed this year.

The $81 billion bill provides aid for communities affected by recent hurricanes in Texas, Florida, Puerto Rico and the U.S. Virgin Islands, as well as wildfires in California.

But passing the bill on Thursday in the Senate would have required the agreement of every senator to speed up consideration of the legislation.

Leadership has struggled to get a deal on previous disaster relief bills over concerns from conservatives that the funding be paid for and jockeying among members looking to get more help for their states.

Cornyn added on Thursday that the disaster relief bill is "a lot more complicated" than the continuing resolution, which the Senate is expected to pass Thursday night.

"Lot more moving parts, lot more varied interests, competition between, you know, various jurisdictions between who gets what, so it's just not likely," he said.