Democrats are holding a temporary funding bill "hostage" by insisting it includes protections for immigrants brought to the U.S. illegally as children, GOP Texas Rep. Jeb Hensarling told CNBC on Thursday.

Republican lawmakers are seeking votes this week for an extension of funding to prevent the federal government from shutting down on Saturday.

Democrats want the bill to include protections for so-called dreamers — immigrants who were brought to the U.S. as children and were protected from deportation by the Obama-era Deferred Action for Childhood Arrivals program. President Donald Trump ordered DACA to end in March unless Congress can come up with a legislative fix.

"This is not a good way to do government," said Hensarling, chairman of the House Financial Services Committee. "[DACA] is an important issue, it needs to be dealt with, but it is not a part of an appropriations bill. It's not funded. It will not expire at week's end."

The spending bill, up for a vote on Thursday, would extend the children's health insurance program, something Democrats had been pushing for. However, many Democrats wanted the DACA protections included.

Republicans hold a 51-49 majority in the Senate and most legislation, including spending bills or an immigration deal, will require 60 votes to pass.

"To hold these issues that are separate ... that Democrats would hold that hostage for a vote in funding our troops I think is unsustainable, unsupportable and at the end of the day I hope it does not happen," Hensarling said on "Squawk Box."

Hensarling said he can't predict whether Republicans will be able to get enough votes to pass a short-term spending bill. "I didn't bring my tarot cards home," he said.

"I don't think the blame" would be on Republicans if the government shutdown, Hensarling added.

—Reuters and NBC News contributed to this report.