Sen. Ted Cruz (R-Tex.), left rear, said he wants a vote on Hurricane Harvey disaster aid without the debt-limit issue attached. (Alex Wong/Getty Images)

Senate leaders are prepared to vote this week on legislation that would pair an increase in the federal government's borrowing limit with $7.9 billion in disaster relief for victims of Hurricane Harvey despite opposition from conservatives.

The decision to combine the two unrelated measures is a potentially risky strategy that could further alienate conservatives who have insisted that any debt-limit increase be paired with corresponding spending cuts. Leaders hope that those on the far right will abandon their demands to immediately replenish rapidly diminishing funds for the Federal Emergency Management Agency.

Sen. John Cornyn (R-Tex.), whose home state is still reeling from Harvey's impact, endorsed the strategy Tuesday and vowed to move quickly to pass the debt-and-disaster package. And House Majority Leader Kevin McCarthy (R-Calif.) said in the Capitol late Tuesday that the House will also take up the measure if it passes the Senate.

"I believe that FEMA is going to literally run out of money at the end of this week," Cornyn told reporters. "It is imperative that we get that supplemental passed. The leaders made the decision to attach the debt limit to that, and I support that decision."

The House is expected to vote on an initial version of the disaster relief package on Wednesday. If all goes as planned, the Senate would then attach the debt-limit increase and hold a vote before the end of the week.

Such a swift timeline would allow Congress to approve the disaster relief money ahead of the potential impact of Hurricane Irma, which could make landfall in Florida this week. It would also allay fears of a federal government default if Congress fails to increase the debt limit.

But conservatives, including Sen. Ted Cruz (R-Tex.), want to see the disaster aid approved without the debt limit attached. Cruz said Tuesday that he believes the FEMA funds should not be "tied to other unrelated matters" but he did not answer when asked if he would actively oppose a plan to combine the two matters. "My hope is that we will see strong bipartisan support for substantial relief from the crushing damages," Cruz said. "There will be many ongoing discussions in Congress about passing that relief package."

President Trump has not explicitly endorsed the plan, but Treasury Secretary Steven Mnuchin said Sunday that both he and the president think that the debt limit should be tied to Harvey funding.

"Our first priority is to make sure that the state gets money," Mnuchin said in an interview on Fox News Sunday. "It is critical, and to do that we need to make sure we raise the debt limit."

Senate Majority Leader Mitch McConnell (R-Ky.) delivered a very similar statement on the Senate floor Tuesday.

"I know that securing this emergency funding is very important for the president," McConnell said. "I know that preventing a default or shutdown amid such a historic natural disaster is also very important to him — and even more so now with another major hurricane on the way."

But leaders of the major House conservative caucuses — the hard-line House Freedom Caucus and the larger Republican Study Committee, have both warned in recent days against attaching a debt-ceiling increase to a Harvey aid package. Rep. Mark Walker (R-N.C.), the RSC's chairman, called the prospect "a little unsettling and even more frustrating" in a Fox News Channel interview Tuesday.

The chairman of the House Freedom Caucus, Rep. Mark Meadows (R-N.C.), said Tuesday that tying the debt limit to disaster aid "is just using it as leverage" but he believes the White House supports McConnell's plan.

"They want the debt ceiling done no matter how it gets done, and I think they support this approach," Meadows told reporters. "I think it's a tactical move that this is the best way to do a debt-ceiling increase, and obviously it will work."

Members of the Freedom Caucus did not take a formal position Tuesday evening on the leadership plan, despite what Meadows called "overwhelming" opposition to the approach.

The roughly 40 Freedom Caucus members would not necessarily have the power to block the legislation. Democrats have generally supported increasing the debt limit in the past, and most Republicans expect that Democrats will do so again.

But if the group decides to vote against the bill it could exacerbate tensions among House Republicans and raise the specter that the bill could pass without a majority of the majority party — violating an informal rule that House Speaker Paul D. Ryan (R-Wis.) had pledged to adhere to when he became speaker in 2015.

Conservative Rep. Joe Barton (R-Tex.), who represents a Dallas-area district, said he is eager to deliver relief for his fellow Texans but he would not say whether he would vote for an aid bill tied to a debt-limit increase.

"I think that's a mistake," he said. "The debt ceiling's a different breed of cat."

Democrats also have not signed off on the plan, in part because Ryan and McConnell have not yet committed to how long the debt-limit increase would last. Senate Minority Leader Charles. E. Schumer (D-N.Y.) and House Minority Leader Nancy Pelosi (D-Calif.) said Sunday that they are willing to consider the plan, but they did not commit to providing the votes necessary to ensure that the bill can pass without conservative support.