"What does it say that staffers would be willing to quit because of the quality of healthcare under ObamaCare would be so poor that they'd rather go somewhere else?" he asked. "I think that speaks volumes."

Cruz added that many other staffers — including those working for Democrats who supported the law — are faced with similar decisions.

"Let me suggest to every member of Congress and every staffer who is feeling that panic — direct that panic not to our own skins, direct that panic to the American people," he said. "Direct that panic to the single mom working at the diner, working two 20-odd hour-a-week jobs who's facing the consequences of ObamaCare."

Cruz spoke as part of a floor speech that is expected to go on for several hours tonight. He took to the floor shortly after 2 p.m. and said he would speak against ObamaCare until he cannot stand anymore.

His remarks are an attempt to persuade members to support language in a House-passed continuing resolution that would defund ObamaCare. But Senate Democrats are hoping to strip that language later in the week with a simple majority vote, which would not require any Republican support.