Story highlights Conservative lawmakers are unhappy with the House GOP health care measure

White House is working on changes, but risk alienating moderate lawmakers

"The House has a current bill that personally I don't think gets the job done," said Ted Cruz

(CNN) Trump administration officials acknowledged to Republican senators at a White House meeting Tuesday that the House bill to repeal and replace the Affordable Care Act is in serious jeopardy.

One adviser to a senator present at the meeting said the acknowledgment was simply that "they don't have the votes to pass this in current form," a reference to whether the House GOP bill in its current form could survive in the Senate.

The meeting included a handful of conservative senators who have expressed deep concerns with the bill. According to multiple aides, Vice President Mike Pence made a short visit to the closed-door briefing with lawmakers.

Another senior Republican aide to a senator in the room said that the White House is "definitely looking at pretty big changes to the Ryan bill."

"There is no possible way a bill can be drafted by an individual or a handful of people and shoved down the throats of 535 people. It doesn't work that way," a Republican senator told CNN, noting that changing the bill is a normal part of the process.

Read More