Boxer introduced her own counter-amendment -- Amendment 622 -- which would create a fund to protect U.S. interests in the Keystone XL decision.
Republicans are countering with amendments of their own, including the idea of making the Patriot Act permanent.
His opponent, Michael Dorf, a law professor at Columbia, countered that the amendment might well not protect pornographic books.
And Senator Sam Brownback, Republican of Kansas, an ardent abortion opponent, had threatened to counter with several amendments of his own.
The defendants' lawyers countered that the amendment didn't empower the federal government to prosecute citizens in such a way; that responsibility remained with state governments.
But critics of the tougher amendment countered that it would cost jobs and take lives by forcing car companies to make lighter, smaller vehicles.
The counter-terrorism Legislation Amendment Bill 2015 was introduced to the Senate on Thursday by attorney general George Brandis and makes a series of changes to the way control orders operate.
The attorney general, George Brandis, said he welcomed the unanimous report on the counter-terrorism legislation amendment bill (No. 1) 2015 and the government would consider its response in consultation with the states and territories.
Under last year's Counter-Terrorism Legislation Amendment (Foreign Fighters) Act the minister for foreign affairs or the minister for immigration can notify the attorney general when a foreign fighter has their passport or visa cancelled on security grounds.
On Wednesday, the House Rules Committee held an emergency hearing to expedite the bill, and it went to the floor under a so-called closed rule, which does not allow for amendments, counter to the promise of more openness made by Speaker John A. Boehner.
Still, Stabenow countered that her amendment was useful in making clear what was actually happening in the name of "honest budgeting".
