WASHINGTON — Even before the House passed the sweeping bill carrying President Donald Trump’s domestic policy agenda, Senate Republicans made it clear that they hoped to make major changes to the legislation before the GOP was done muscling it through Congress.

Several have wanted to pare back the cuts to Medicaid, the health care program for the poor, that House Republicans envisioned in the version of the legislation that they approved late last month. A handful have sought to salvage tax credits incentivizing clean energy projects that the House measure would repeal. Many have pushed to grant companies prized tax breaks for the long run, not just for a few years, as their colleagues across the Capitol opted to do.

The problem senators face is that each of these changes would be expensive. At $2.4 trillion, the cost of the legislation that barely passed the House is already huge. So Senate Republicans are now hunting for ways to save money, a hazardous task that could involve shaving the ambitions of their colleagues in the House or in the White House.

On the chopping block are some of Trump’s favorite parts of the bill, like not taxing overtime. Republican lawmakers have long been skeptical of some of the president’s tax ideas, with the view that the populist policies will not spur the economy like traditional supply-side conservatism can.

“I think it all comes down to what we’ve got to pay for,” Sen. Thom Tillis, R-N.C., said. “At the end of the day, we’ve got to pay for pro-growth policies.”

The debate is in some ways a classic one on Capitol Hill, where throughout history and without regard to political party, senators have been reluctant to defer to their colleagues in the House, and vice versa.

“It’s the Senate, so the Senate is going to do what it damn well wants to do, and that’s a good process,” Sen. Ted Cruz, R-Texas, said at a Punchbowl News event Wednesday, where he warned that his chamber would pass a bill “markedly different” from the House measure, pushing enactment of the package well past his party’s July 4 deadline.

To top Senate Republicans, the most economically powerful tax cuts incentivize companies to make new investments and conduct research. Accelerated depreciation schedules, though, do not grab political attention the way Trump’s promises for “no tax on tips” did, so the House version of the bill only included the business tax breaks through 2029.

Senate Republicans want to make the business write-offs a permanent feature of the tax code, a change that they and some economists believe would help encourage more companies to expand. As one way to cover that cost, Senate Republicans are looking at ways to further curb eligibility for a tax cut for overtime pay, including by setting a lower income ceiling for the break and by more strictly defining what counts as overtime, lawmakers said.

“Obviously, there’s a lot of dials, whether you’re talking about no tax on tips, overtime, any of those,” said Sen. Roger Marshall, R-Kan.

“How many years did they go? At what level do they stop?”

Sen. Bernie Moreno, R-Ohio, a former car dealer, wants to tighten the House plan for allowing Americans to deduct up to $10,000 in interest on car loans, which would apply to vehicles made in the United States, including used and new cars, as well as all-terrain vehicles and recreational vehicles. Moreno is proposing to limit the tax break, one of Trump’s campaign promises, just to loans for new cars.

“We save a lot of money. An RV? Motorcycles? ATVs?” he said. “That’s not the idea; the idea is to help working Americans be able to afford a car.”

Senate Republicans are searching for cuts because of growing concern among some conservatives, as well as on Wall Street, about the bill’s impact on the country’s fiscal situation.

While paring back some of Trump’s campaign promises could help keep the cost of the legislation near what it was in the House, some lawmakers are calling for much deeper spending cuts.

Sen. Ron Johnson, R-Wis., has been loudly calling for the legislation, which already includes roughly $1.8 trillion in spending reductions, to slash trillions more. His complaints won him a meeting with top White House officials, including Vice President JD Vance, at the Capitol this week.

Johnson’s pitch is to remove all of Trump’s new tax priorities from the bill and instead focus the legislation exclusively on extending expiring tax cuts from 2017, cutting spending and raising the debt ceiling.

Republicans could then tackle White House priorities, and further spending cuts, in a second piece of legislation, Johnson argues.