The Club for Growth and a collection of 45 conservative groups is demanding Republicans repeal all of Obamacare's taxes after reports indicated senators may keep some of them around.

The groups sent a letter Tuesday to Sen. Orrin Hatch, R-Utah, chairman of the Senate Finance Committee, calling for repeal all of the taxes imposed by Obamacare.

"Recent media reports suggest that the Senate may be wavering on repeal of these taxes. This would be a mistake," according to the letter.

It featured groups such as Americans for Tax Reform, Taxpayers Protection Alliance and American Consumer Institute.

So far, Republicans have not decided what they want to do on all of Obamacare's taxes but some appear likely to go away.

Sen. John Thune, R-S.D., the third-ranking GOP senator, said it appears likely the law's consumer taxes, such as the medical device tax, will be cut. But he previously didn't make a commitment on the fate of the law's "Cadillac" tax on high-cost health plans.

Sen. John Cornyn, R-Texas, said there hasn't been a consensus yet on the taxes.

"That remains to be decided," he told reporters Tuesday.

The conservative groups say the final Senate package should "retain the broad tax relief that was included in the House passed American Health Care Act."

It claimed the law's taxes "directly suppress economic growth."

But the GOP Senate is grappling with how to pay for more generous offerings in its version of the AHCA. Some more centrist Senators are pushing for a more gradual phase out of the law's Medicaid expansion and more generous tax credits than the AHCA.

The Senate hasn't made a deadline for passing its version of the AHCA. Leadership has hoped to get a vote by the July 4 recess but that isn't a hard and fast deadline.