The root of the problem predates Mr. Trump. For years, Congress has jammed through huge omnibus spending bills that set funding for an entire fiscal year in the final days of legislative sessions. Lawmakers have also passed a patchwork of short-term spending bills to keep the government from shutting down, which has happened three times during the Trump administration. And while presidents have always had the power to transfer and reallocate funds, Mr. Trump has made far wider use of that authority to subvert the will of lawmakers.

The administration is expected to announce another diversion of funds to help pay for construction of a wall on the southern border, Mr. Trump’s signature campaign promise, in the coming months. The president declared a national emergency last year to allow him to use money not appropriated for the wall to build it.

And while the Senate acquitted Mr. Trump this month of impeachment charges stemming from his decision to withhold military funding from Ukraine, the Government Accountability Office, a nonpartisan federal watchdog, found that Mr. Trump’s actions violated the Impoundment Control Act, which limits a president’s ability to refuse to spend money allocated by Congress.

Several lawmakers, including some who are still deeply involved in crafting the dozen must-pass spending bills each year, acknowledge that the annual fiscal process no longer works as it once did. A large factor, several say, is the demise of earmarks, the power to steer money to lawmakers’ pet projects in order to persuade them to take tough votes. Long scorned as a tool of corruption, Congress ultimately banned the practice after a series of scandals that culminated in the imprisonment of the lobbyist Jack Abramoff.

“When earmarks were around, they gave members a reason to pay attention to appropriations — they always knew they had some skin in the game,” said Mr. Kelly, who co-wrote a book about earmarks and their benefit to democracy. “By being penny-wise, we’ve sort of been pound-foolish.”