(Mark Wilson/GETTY IMAGES)

Updated 2:30 p.m.

House Speaker John Boehner (R-Ohio) on Thursday reiterated his message on the debt-ceiling fight, pledging that Republicans will not give the White House “a blank check” to raise the country’s borrowing limit without significant spending cuts and structural reforms.

But Boehner declined to detail either a specific timeline for the trillions of dollars in cuts he has proposed or a particular spending-cap proposal, such as the one outlined by Sens. Claire McCaskill (D-Mo.) and Bob Corker (R-Tenn.)

Boehner’s comments came shortly before Senate Republican Leader Mitch McConnell (R-Ky.) said he wants a deal to cut agency spending over the next two years and make significant changes to Medicare and Medicaid.

Boehner also pushed back against his critics and stood by his call for greater spending cuts than the amount by which the debt ceiling will be raised this summer.

“Clearly, we struck a nerve,” Boehner said, adding that the responses from the White House and Democrats have been “panic and hysteria.”

“I believe that if we don’t act boldly and act boldly now, the markets will act for us pretty soon,” Boehner said at his weekly news conference. “Remember that Standard and Poor’s warned several weeks ago that it might downgrade the United States debt – not over the debt-limit fight, but because Washington has no plan to deal with our national debt. The greatest threat to our economy, to job creation and to our children’s future is doing nothing.”

On Monday, Boehner called in a speech at the Economic Club of New York for more than $2 trillion in spending cuts in order for Republicans to support any measure to raise the country’s $14.3 trillion debt ceiling, which the Treasury Department estimates will be reached by Aug. 2.

As he did on Tuesday, Boehner on Thursday said that Republicans are opposed to the inclusion of tax increases in the ongoing deficit-reduction talks with the White House. Congressional negotiators from both parties met with Vice President Biden and other administration officials on Tuesday, their second meeting aimed at reaching a deal on a debt-reduction plan.

In addition to spending cuts, Boehner has also advocated for structural reforms in the country's budgeting process. But asked Thursday whether he supported the McCaskill-Corker spending cap, which would limit federal spending to 20.6 percent of GDP, Boehner said he would not yet commit himself to a particular plan.

“I do think there is going to have to be budget-process reforms,” he said. “I don’t want to tie myself down in terms of what those are. But I don’t want phony caps; I don’t want phony targets. We know what the challenges are; why don’t we just tackle the problem?”

The White House and Democratic leaders have taken aim at the spending cap proposal, arguing that it could lead to sweeping changes to federal entitlements and other programs.

At a CBS News town hall broadcast Thursday, President Obama repeated his proposal a provision that would automatically impose tax increases and spending cuts to balance the federal budget.

House Democrats responded to Boehner’s claims Thursday by noting that 60 leaders of business groups have written a letter to congressional leaders urging for the debt ceiling to be raised.

“In making this recommendation, we remain extremely concerned about the level of the federal debt and large annual budget deficits and remain committed to working with you and the Administration to address our Nation’s fiscal challenges,” wrote the business groups, among which are the U.S. Chamber of Commerce and the Business Roundtable. “Tough calls on U.S. spending must be made as part of a debate about the budget and we agree that restoring balance to our fiscal position will require that the government spend less and spend more wisely.”

One of the looming questions in the debt-limit fight is the timeframe over which House Republicans would like to see their proposed trillions of dollars in spending cuts enacted. A shorter timeline would lead to more sweeping cuts.

On the timeline issue, Boehner said Thursday that those details are yet to come.

“I think it’s a little too early – I’m not going to lock myself into what kind of timeframe,” Boehner said, adding that “over the next coming weeks,” there will be more opportunities to discuss the specifics of the spending fight.

Senate Republicans are meeting at the White House Thursday to discuss the road ahead on deficit reduction with administration officials, one day after Senate Democrats held a similar huddle.

Staff writer Paul Kane also contributed to this story.