But Republicans are struggling with the vote. Conservatives such as Mr. Lee and Senator Rand Paul of Kentucky — another Republican who says he will vote for the resolution of disapproval — believe that members of Congress have ceded far too much power to the executive branch over the years in an effort to avoid taking politically tough stances themselves. Republicans regularly accused President Barack Obama of executive overreach on issues such as immigration, health care and the environment and now risk being accused of hypocrisy if they stand by while Mr. Trump ignores Congress to do as he wishes.

Many Republicans believe that allowing Mr. Trump to redirect money at his own discretion after Congress explicitly forbade it would amount to a final acquiescence to the executive branch that could set a precedent for future Democratic presidents. But they are also in no rush to irritate a president who has shown vast capacity to stir Republican voters or to rile the activist groups that back him.

On Wednesday, The Hill newspaper reported that conservative groups such as the Club for Growth were considering backing a primary challenge next year to Senator Thom Tillis, Republican of North Carolina, because of his opposition to Mr. Trump on the emergency declaration and other issues.

Looking for a way to not anger Mr. Trump and salvage some congressional pride, Mr. Lee introduced his proposal that would require Congress to approve any emergency declaration or it would terminate after 30 days at most. That would mean approval by Congress would be required rather than the current arrangement in which Congress is given the option of disapproving an emergency declaration and the president can veto it. Under the current legislative arrangement, Congress can block an emergency declaration only if opponents can muster the two-thirds vote to override a veto.

“If we don’t want our president acting like a king, we need to start taking back the legislative powers that allow him to do so,” Mr. Lee said.

The Lee bill, however, would have no impact on the president’s current emergency declaration. Republicans saw it as a way to both back Mr. Trump and close the door to future use of the declarations by presidents — notably Democratic presidents — to circumvent Congress.