The Club for Growth and the Madison Project also pressed lawmakers to back Cruz' effort.
The issue has roiled the Republican Party, exacerbating the divide between tea party conservatives and GOP incumbents who repeatedly have voted against the health care law but now find themselves on the defensive. Republican senators said defunding Obamacare simply won't happen with a Democratic president and Democrats controlling the Senate.
"It will be a cold day in Gila Bend, Ariz., before we defund Obamacare," said Sen. John McCain, R-Ariz., the party's 2008 presidential nominee. "A very cold day. In fact there may be a snowstorm. ... I know how this movie ends. I don't know all the scenes before it ends, but I know how it ends. We don't defund Obamacare."
Associated Press writers Andrew Taylor, Alan Fram, David Espo and Laurie Kellman contributed to this report.