Sen. Barbara BoxerBarbara BoxerAnother day, another dollar for retirement advice rip-offs Carly Fiorina 'certainly looking at' Virginia Senate run Top Obama adviser signs with Hollywood talent agency: report MORE (D-Calif.) said Thursday that while Sen. Ted CruzTed CruzNet neutrality fight descends into trench warfare Secret Service: No guns at Trump NRA speech Cruz: Breaking up 9th Circuit Court ‘a possibility’ MORE (R-Texas) says Congress must protect people from ObamaCare, she sees it as her job to protect the American people from Cruz.

Boxer acknowledged on the Senate floor that ObamaCare had a "very, very tough rollout" in its early weeks. But she said more than two million people have now enrolled in a health plan under ObamaCare, and said Cruz is trying to get people to forget that.

"You wouldn't know that because Senator Cruz keeps saying over and over again, 'what have the Democrats in the Senate done to protect people from ObamaCare?' " she said. "Well, I gotta protect the people from him, because if he had his way, he'd repeal ObamaCare.

"While Senator Cruz says we've done nothing to protect the people, the opposite is true. We stand in support of the people."

Boxer read a few letters from constituents who are now able to buy insurance under the ObamaCare exchanges, and said she would not let Republicans repeal the law.

"I'm not going to let Senator Cruz take away his insurance," she said after reading one constituent letter.

Boxer spoke after the Senate approved a $1 trillion spending bill for the rest of 2014. Just before that vote, Cruz asked for unanimous consent to add two amendments to defund ObamaCare for 2014, but Democrats rejected both of those requests.

Despite Boxer's comments, Cruz argued that ObamaCare has led to higher premiums, canceled policies and reduced job opportunities due to requirements that companies must offer their full-time workers an insurance plan. He also said there is no denying these adverse impacts, and said Congress has no excuses not to repeal the law at this point.

"The essence of irresponsibility is seeing a harm and seeing the facts, and refusing to act," Cruz said.