To soar far away from Earth and even on to Mars, NASA has dreamed up the world’s most powerful rocket, a behemoth that borrows from the workhorse liquid-fuel rockets that sent Apollo missions into space four decades ago.

But with a price tag that some estimate at $35 billion, it may not fly with Congress.

NASA Administrator Charles Bolden and several members of Congress on Wednesday unveiled the Obama administration’s much-delayed general plans for its rocket design, called the Space Launch System. The multibillion-dollar program would carry astronauts in a capsule on top, and the first mission would be 10 years off if all goes as planned. Unmanned test launches are expected from Cape Canaveral, Fla., in six years.

Calling it the “largest, most powerful rocket built,” NASA’s exploration and operations chief, William Gerstenmaier, said the rocket will be tough to construct. But when NASA does it, “we’ll have a capability to go beyond low-Earth orbit like no other nation does here on Earth,” he said in a telephone briefing Wednesday.

The rocket resembles those NASA relied on before the space shuttle, but even its smallest early prototype will have 10 percent more thrust than the Saturn V that propelled Apollo astronauts to the moon. When it is built to its fuller size, it will be 20 percent more powerful, Gerstenmaier said. That bigger version will have the horsepower of 208,000 Corvette engines.

NASA is trying to remain flexible on where it wants to go and when. The space agency is aiming for a nearby asteroid around 2025 and then on to Mars in the 2030s. There could even be a short hop to the moon, but not as a main goal. All those targets require lots of brute force to escape Earth’s orbit, something astronauts have not done since 1972.

The far-from-finalized price tag may be too steep given federal budget constraints.

“Will it be tough times going forward? Of course it is,” Sen. Bill Nelson, D-Fla., said in a separate news conference. “We are in an era in which we have to do more with less — all across the board — and the competition for the available dollars will be fierce. But what we have here now are the realistic costs” verified by independent experts.

Although five senators of both parties who are leaders in science issues praised the plan in a joint press release, outside experts are skeptical that Congress will agree to such a big spending project.

“In the current political environment, new spending is probably the most taboo thing in politics,” said Stan Collender, a former Democratic congressional budget analyst. He put the odds of this getting congressional approval at “no better than 50-50 this year. There are going to be a lot of questions asking what kind of commitment we’re going to be making here. You can find yourself with a rocket that no one wants to fire.”

Nelson puts the cost of the program at about $18 billion over the next five years. But that estimate is mostly for development and design through the first test flight in 2017, and doesn’t include production of later rockets, Gerstenmaier said. Gerstenmaier wouldn’t give a total estimate, but it is almost double that, according to senior administration officials, who spoke on the condition of anonymity because they were not authorized to make the announcement.

University of Texas engineering professor Hans Mark, a former NASA deputy chief and frequent critic of recent space agency plans, said money and where the rocket is going are likely to be bigger problems than technical engineering issues. He said that in some ways, it sounds like NASA is melding the best of space shuttle and Apollo technologies.

The rocket is similar to Apollo not only in size and shape, but in its reliance on liquid fuel. The winged, reusable and recently retired space shuttles sat on top of a giant liquid fuel tank, but relied heavily on twin solid rocket boosters to get off the ground.

NASA figures it will be building and launching about one rocket a year for about 15 years or more in the 2020s and 2030s, according to the senior officials. The idea is to launch its first unmanned test flight in 2017 and send up the first crew in 2021, followed by the asteroid and Mars missions.

At first, the 320-foot-tall rockets will be able to carry 77 to 110 tons, which would include the six-person Orion Multi-Purpose Crew Vehicle capsule and more. The crew capsule, which is now being built, has at least twice as much space as the old Apollo capsules, which could only fit three astronauts, said NASA spokesman Michael Braukus.

Eventually the rocket will grow to 400 feet tall, weigh 3,250 tons and be able to carry another 143 tons into space, maybe even 165 tons, the officials who spoke on condition of anonymity said. By comparison, the long-dormant Saturn V booster that sent men to the moon was able to lift 130 tons.

The plans dwarf the rumbling liftoff power of the space shuttle, which could haul just 27 tons. The biggest current unmanned rocket can carry about 25 tons.

Some of the design elements, the deadline and the requirement for such a rocket were dictated by Congress. Senators were talking about issuing subpoenas to NASA because they felt the space agency was taking too long in coming up with the design, but NASA officials said they just wanted to get all the details right before unveiling the plan.

The giant rocket will be powered by liquid hydrogen and liquid oxygen fuel. During the initial test flights, it will use solid rocket boosters designed for the shuttle strapped on its outside, and will have shuttle main engines powering it on the inside. But soon after that the solid rocket boosters will be replaced with new boosters that should have advanced technology and may be either liquid or solid.

NASA hopes to free up money for the rocket by turning over the launching of astronauts to the International Space Station, which orbits the Earth, to private companies and just rent spaces for astronauts like a giant taxi service. NASA officials aren’t sure how much they’ll save because it depends on how much the firms will charge and when they will start flying.

Stanford University engineering professor Scott Hubbard worries that NASA has a history of spending far more than initially proposed — the space shuttle cost about twice what it was supposed to — and that this new rocket system will drain money from other NASA missions. NASA already has major financial overruns with the still-under-construction, multibillion-dollar replacement for the Hubble Space Telescope.