A conservative House member who last week led the fight from the right against a temporary spending measure designed to keep government running through mid-November is not committing to backing a deal reached Monday intended to resolve the dispute.

A spokeswoman for Rep. Jeff Flake (Ariz.) sidestepped a question about whether the lawmaker will return to Washington on Thursday to object during a key House vote on the compromise.

“Congressman Flake is still reviewing the bills,” Genevieve Rozansky said in response to the inquiry.

The deal relies on a two-step approval process in the House to keep the government running, necessary because House members are on recess this week in observance of the Jewish new year.

First, the House will consider a resolution to keep the government open through next Tuesday — designed to allow the chamber to use a voice vote that does not require all members to be present.

The House will then hold a full vote on a longer-term bill to provide funding into November when members return next week.

The entire deal could be thrown into disarray, however, if even a single House member returns to Washington on Thursday and objects to the voice vote. That would require the chamber to hold a roll call, exceedingly difficult while most members are scattered around the country for the recess.

House Speaker John A. Boehner (R-Ohio) briefed his caucus on the deal in a Monday evening conference call. According to a leadership aide, no House Republicans indicated that they might object to the plan.

Flake and other conservatives will be under intense pressure to let the deal go through on Thursday. Any member who objects could be blamed if the issue is not resolved in time to prevent a government shutdown Oct. 1.

Plus, members who object to the terms of the stopgap funding measure will be able to vote against it next week. The measure is expected to gain enough support from Republicans and Democrats to ensure its passage, even if a sizable number of conservatives are opposed.

But Flake has a history of bucking his party’s leadership on spending issues. Last week, he led an effort by conservatives to oppose the appropriations measure because he did not think it cut government spending deeply enough.

The bill was unexpectedly defeated on the House floor Wednesday when 48 Republicans voted against it and Democrats withheld their votes over spending cuts Republicans had imposed to offset the cost of increased disaster relief.

By Thursday, Boehner persuaded 24 Republicans to switch position and support the bill, allowing it to pass. That paved the way to Monday’s deal in the Senate.

But Flake was not among the persuaded, and he voted “no” a second time.

The bill sets spending at $1.04 trillion for the year, a level agreed to by Republicans and Democrats at the end of the bitter August fight to raise the nation’s debt ceiling.

Flake and others argue that the debt deal set an appropriations ceiling and Republicans should seek to spend less. Although the short-term funding measure cuts spending by 1.5 percent from the fiscal year that ends Friday, it would still allow the government to spend $24 billion more than a budget House Republicans approved in April.

“Despite strong rhetoric calling for austerity, merely a month after the debt-ceiling deal was passed, Congress is back to increasing spending,” Flake said after voting against the bill last week. “This is not what we should be doing.”