• Elon Musk and Vivek Ramaswamy are seeking major cuts to federal spending.
• Any meaningful reductions will be near impossible without legislation to cut Social Security benefits, Medicare and Medicaid — long considered a third rail in Congress.
• The duo had a day of meetings on Capitol Hill with hundreds of Republican lawmakers.

WASHINGTON — Entrepreneurs Elon Musk and Vivek Ramaswamy have an ambitious agenda to cut federal spending with the help of their outside advisory council, the Department of Government Efficiency (DOGE).

But on their first joint visit to Congress on Thursday, the pair also likely saw some of the limits of outside influence on the workings of the legislative branch.

Crisscrossing Capitol Hill together on a marathon day of meetings with lawmakers, Musk and Ramaswamy got warm welcomes from Republicans.

Their overall message was popular, too: A smaller federal government, looser regulations and a private sector approach to the public sector have long been cornerstones of conservative governance.

But there was also an elephant in the rooms they visited: An unspoken understanding that Musk's stated goal of slashing federal spending by $2 trillion is already DOA.

The reason for this comes down to math.

In fiscal 2023, for example, the federal government spent a total of $6.1 trillion, according to the nonpartisan Congressional Budget Office.

Of that $6.1 trillion, about $3.8 trillion was already off limits for cuts on day one, legally obligated to go toward mandatory spending programs like Social Security benefits for retired workers, Medicare coverage and veterans benefits.

After that, roughly $650 billion was set aside to pay the interest on the national debt.

This left $1.7 trillion for everything else, known as discretionary funding. $805 billion of this was spent on national defense, a largely untouchable pot of money. Finally, the remainder was divided up among the federal departments that perform much of the visible, daily work of government, agencies like FEMA, NASA, and Customs and Border Protection.

While Musk and Ramaswamy went from meeting to meeting, Republicans close to the government funding process, like House Appropriations Committee member Rep. Steve Womack, Ark., said that while some cuts were possible, the $2 trillion that Musk talks about would likely be a bridge too far.

"If you're going to leave the social safety net programs alone and not touch them, that means you're going to try to cut hundreds of billions of dollars out of discretionary spending" if you want to achieve massive, DOGE-style reductions, he told CNBC in an interview.

"It would be very difficult to do that without cutting national security," said Womack.

Even proposing small cuts or changes to mandatory programs like Social Security, Medicare or Medicaid can prove politically dangerous for members of Congress who must run for reelection every few years.

Nonetheless, some Republicans are open to considering limited reforms to these programs. House Majority Leader Steve Scalise of Louisiana, for example, said he was open to exploring potential work requirements for Medicaid recipients, and requiring stricter verification for Social Security benefits.

"Those are the kinds of things that we're also going to be looking at," Scalise told reporters after his meeting with Musk and Ramaswamy.

House Speaker Mike Johnson, R-La., kept expectations low, saying Thursday's meetings with Musk and Ramaswamy were "brainstorming" sessions, a chance to float some ideas with no pressure to reach a consensus.

Only when Republican President-elect Donald Trump takes office in January, and Senate Republicans take control of their chamber, can plans really begin to move ahead.

Cutting spending will not be easy. Johnson's hair's breadth of a vote margin means he will only be able to afford a few defections from his conference on any given bill, and still pass it on a party-line vote.

Some Republicans have begun to coalesce around a different way to cut government costs: by requiring federal employees to come back to the office in person five days a week. 

"One of the things I'm most excited about is requiring people to show up for work," Sen. John Cornyn, R-Texas, told reporters. "And if they don't, then they can voluntarily leave and we can save a lot of money."

Sen. Susan Collins, R-Maine, the Senate's top appropriator, also embraced the idea of calling federal employees back into the office. "It's amazing to walk through some federal buildings," she said, "and it's just empty offices everywhere."

"If the federal government's truly going to change the way people work, then we've got [to address the] excess buildings and space," said Collins.

Sen. Joni Ernst, R-Iowa, who leads the newly created Senate DOGE Caucus, also highlighted the issue of underutilized federal office space due to employee telework in a new report she unveiled Thursday at the first Senate DOGE Caucus meeting.

"Over $81 million is being wasted every year for the underutilized government office space alone," the report found.

Yet findings like this also serve to underscore how limited the impact of changes to federal office space would be on the massive spending cuts that Musk is looking for.

Nonetheless, the idea is gaining steam in the GOP. Federal return-to-work policies were the most frequently mentioned example of potential cost cutting by Republicans who spoke with CNBC on Capitol Hill this week.

It is not clear yet whether federal employees would quit en masse if they were forced to come back into the office five days a week, thereby freeing up their current salaries for other uses.

What is clear, however, is that unions representing hundreds of thousands of federal workers nationwide are gearing up to fight any effort to change their members' working conditions.

For the DOGE team, these battles could present a whole new set of challenges.

Correction: This story has been updated to correct the name of the U.S. Customs and Border Protection agency.