House Republicans are under pressure from business and Tea Party groups to quickly pass the budget adopted by the Senate Thursday night to save weeks of time, and to more quickly get to a tax reform bill.

Doing so would mean leaving out language creating a special vehicle for billions of dollars in spending cuts, something House conservatives fought hard to keep in the House version of the budget.

But if the House simply passed the Senate budget, Republicans could be ready to unveil tax reform in days. Tax reform is meant to proceed through the special reconciliation process unlocked by the budget, which would block the Democrats from filibustering in the Senate.

Speaking Friday morning on Fox News, House Ways and Means Committee Chairman Kevin Brady said events could play out on that accelerated timeline.

"There's a very clear possibility that the House clears this next week," the Texas lawmaker said of the Senate budget. After the budget is finalized, he said, he would set a date for unveiling tax reform legislation and for a mark-up of the bill at the committee.

Thursday night's bill included changes not only to make the Senate budget more viable in the House, but also to streamline the tax reform process once it gets going. That seemed to excite Republicans about the possibility of quickly moving on tax reform, even if the budget didn't include similar reconciliation language letting the GOP move a bill on spending cuts just as quickly. The House budget includes reconciliation instructions for $203 billion in spending cuts.

"They shaved two to three weeks off the legislative process, which really still preserves the possibility that they're going to get something done this year" on tax reform, Rohit Kumar, leader of PwC's Washington National Tax Services and a former staffer to Senate Majority Leader Mitch McConnell, said on CNBC Friday about the Senate version.

FreedomWorks, an outside conservative group, called on the House GOP to move forward with the Senate budget next week. "We urge the House to quickly move to adopt the Senate resolution and for all lawmakers to stand up to the armies of lobbyists threatening to derail historic tax reform – our tax code should work for everyone," the group's vice president of policy Nathan Nascimento said in a statement.

In an email to the Washington Examiner, Heritage Action vice president Dan Holler said that the conservative group is "supportive of the Senate-passed budget because it moves us towards tax reform."

"On a parallel track, Republicans need to begin seriously tackling America's long-term spending challenges," Holler added. "Every single one of them ran campaigned on it, and inaction -- or worse, a renewed spending binge -- is completely unacceptable."

The U.S. Chamber of Commerce, the biggest business group, also called on House Republicans to simply pass the Senate budget.

"The business community urges the House to quickly take up and pass the Senate measure," the organization's chief policy officer Neil Bradley said.