It also gave private industry the role of building space vehicles to take humans to the International Space Station (ISS).
'Relying with Russia'
The former astronauts said in the letter released to NBC News that in the future those travelling to the ISS would only be able to do so by hitching a ride on Russia's Soyuz spacecraft "at a price of over $50m per seat".
"For the United States, the leading space faring nation for nearly half a century, to be without carriage to low Earth orbit and with no human exploration capability to go beyond Earth orbit for an indeterminate time into the future, destines our nation to become one of second or even third rate stature," they wrote.
"The availability of a commercial transport to orbit as envisioned in the president's proposal cannot be predicted with any certainty but is likely to take substantially longer and be more expensive than we would hope."
Obama is expected to set out plans to accelerate development of a large, heavy-lift rocket to carry astronauts beyond low-earth orbit when he speaks on Thursday.
He will also declare that orbiting Mars is an eventual goal for the space programme.
Obama will also salvage the crew capsule Orion, which under Constellation was to carry astronauts to the moon, and it will serve as an emergency escape vehicle at the International Space Station.
That would free American astronauts from having to rely on Russia's Soyuz capsule to return to Earth in an emergency.
However, the White House on Wednesday defended the decision to scrap the rest of the Constellation programme.
Robert Gibbs, the White House spokesman, said an independent commission had determined the programme was "years behind schedule, massively over-budget, that we weren't going to meet the timeframe of going to the moon under any circumstance".
The new plan will mean more jobs, greater investment in innovation, "more astronaut time in space, more rockets launching sooner, and a more ambitious and sustainable space programme," he said.
The Obama administration estimates the new plan would create an estimated 2,500 jobs in the US, but the end of Constellation to see about 9,000 jobs lost at the Kennedy Space Centre.
The White House's new policies have found support from one former astronaut, Buzz Aldrin, the man who followed Armstrong on to the Moon.
"I continue to be excited about the development of commercial capabilities to send humans into low-earth orbit and what this could ultimately mean in terms of allowing others to experience the transformative power of spaceflight," he said in a statement.