The Trump administration just made some massive promises about the GOP's Obamacare replacement that will be hard to keep

Health and Human Services Secretary Tom Price said Tuesday that the new House GOP plan to overhaul the American healthcare system will bring down the cost of premiums and the cost of healthcare in the US while not increasing the federal deficit.

"We believe strongly that through this process and as it takes effect, that we will see a decrease in not only the premiums that individuals will see but a decrease in the cost of healthcare for folks," Price said, appearing at the White House press briefing.

Price's promises about the House Republican proposal, which has already run into intraparty criticism, will be difficult to keep.

That's because total healthcare spending - based on the Centers for Medicare and Medicaid Services' National Health Expenditure Account - has never gone down year-over-year since 1961, increasing be an average of 9.1% annually over that time.

Additionally, the period of time following the passage of the Affordable Care Act saw the annual increase in healthcare expenditures slow to its lowest level since the data began, with an only 2.9% increase in 2012.

Finally, premiums have similarly been increasing for years - and, under the ACA, have slowed their rise.

From 2001 to 2006, average monthly premiums for family of four increased by 63%. From 2006 to 2011, that number fell to 31%. And from 2011 to 2016, there was an increase of 20%, according to an analysis by the nonpartisan Kaiser Family Foundation.

Premiums have not decreased on a year-over-year basis since at least 2000.

Price also said that the "goal and desire" of Republicans is that the AHCA would not increase the federal deficit. Such a goal comes despite the fact that it keeps large payments for insurance while also repealing taxes that helped pay for those expenses.

"I know the goal and desire of those on the hill is that this does not increase the cost to the federal government," Price said.

The Joint Committee on Taxation, a nonpartisan congressional analysis office, estimated in a release Tuesday that the AHCA would lose roughly $500 billion in revenue for the federal government over the next 10 years.