That might come as a surprise to Republicans who sought reassurance from their leadership regarding compromises made with Democrats, as well as the deal’s appointment of a committee tasked with putting together a deficit package later this year.

Debt-ceiling negotiations between the White House and Republican leaders stalled in part because Republicans refused to agree to tax hikes, while President Obama and the Democrats pushed for increased revenue as part of a “balanced approach” to solving the deficit.

In the debt-limit deal that Obama ultimately signed into law earlier on Tuesday, Congress gave permission to raise the debt ceiling by $2.1 trillion, while also making nearly $1 trillion in deficit cuts over 10 years and establishing a 12-member, bicameral committee charged with putting together an additional $1.5 trillion deficit-reduction package.

The legislation also includes “punishments” in the case of a deadlock in the committee or failure to act by Congress. Congress failing to act on the recommendations by Christmas would trigger $1.2 trillion in across-the-board spending cuts divided evenly between defense and non-defense spending.

Likely referring to that aspect of the agreement, Reid said, “If [Republicans] don't like [including revenues], then they can look forward to the huge cuts that will take place in sequestration dealing with defense and some of their other programs will be cut, including mandatory programs, farm programs and things of that nature.”

The proposed defense cuts prompted at least one prominent Republican senator to vote no on the bill. Sen. Lindsey GrahamLindsey Olin GrahamGOP and Dems bitterly divided by immigration We are running out of time to protect Dreamers US trade deficit rises on record imports from China MORE (S.C.) said he could not support the deal in part because it weakened the defense infrastructure. Others, such as House Armed Services Committee Chairman Buck McKeon (R-Calif.), voted for the proposal despite “deep reservations” over possible harm to military services.

Concern over the so-called “super committee” had also been raised on both sides of the aisle. Republican leaders in the House and Senate assured their party that tax increases could not pass the committee, or at the very least would be shot down in the Republican-controlled House.

“The chances of any kind of tax increase passing with this, with the appointees that John BoehnerJohn Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery MORE and I are going to put on there, are pretty low," Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellGOP strategist donates to Alabama Democrat McConnell names Senate GOP tax conferees Brent Budowsky: A plea to Alabama voters MORE (R-Ky.) said Monday.

However, the White House has maintained that the long-term approach to cutting the deficit must include entitlement reforms and increased revenues. “The suggestion that it is impossible for the joint committee to raise tax revenue is simply not accurate; it’s false,” White House press secretary Jay Carney said in his briefing Monday.

Committee appointments will be shared between Republican and Democratic leaders in both chambers of Congress and have yet to be announced. The committee is expected to present its recommendations by Thanksgiving.