Mr. Tester and Mr. Walz have shown that they are willing to maneuver their caucuses toward compromise if the Republican position is within range. To pass the accountability legislation, a long-held priority for both parties that had the support of influential veterans’ groups, the Democrats had to overcome initial opposition to weakening the protections afforded to department employees accused of wrongdoing. The changes were opposed by the largest federal workers’ union. The final legislation, which Mr. Trump signed into law late last month, makes it easier for the department to fire problematic employees, incentivizes whistle-blowing and gives the secretary greater hiring authorities to fill vacant medical center director jobs.

Legislation that overhauls the department’s appeals procedure was an easier lift. About half a million veterans have pending claims contesting a Veterans Benefits Administration decision. The process, as currently configured, can take years to sort out. The legislation tries to significantly expedite that process by creating distinct queues for veterans based on the evidence they wish to submit with their claims.

The department had championed a similar proposal during the Obama administration, and it won support from the veterans groups. But then lawmakers ran out of time to move it through Congress. The legislation won quick passage in the House this term and, with Congress returning from recess, is expected to win passage in the upper chamber as well. Lawmakers hope it will become law before the August recess.

The good feeling may soon be put to the test, however. “What they are getting done now is low-hanging fruit,” said Paul Rieckhoff, the chief executive of the Iraq and Afghanistan Veterans of America. “You could argue it is a great political strategy: Get points on the board, get wins. But I don’t think that’s going to last.”

Mr. Rieckhoff was referring to negotiations, which are expected to intensify this fall, over a reimagining of the multibillion-dollar Choice program and a half dozen other programs that allow veterans to seek health care in their communities at government expense. In the aftermath of the 2014 scandal, lawmakers created a program that gave veterans facing long wait times and travel distances the option of going to private doctors. But lawmakers from both parties agree that its unnecessarily cumbersome scheduling and payment process, among other problems, needs fixing.

Exactly how to do so is where the fights might occur. Democrats support community care in theory, but they are fearful that Republicans in the majority and the White House could try to use a significant expansion of the program to force further privatization of the department’s services. Republicans largely deny that that is their agenda. Mr. Shulkin plans to present lawmakers with the department’s own plan, which could either heighten animosities or dampen them.

“If they simply reauthorize Choice resources at the current level, that achieves bipartisan consensus easily,” Mr. Carter said. “If they revamp Choice to make it more aggressive, the fiscal implications of that will make many Republicans balk and the privatization implications will make Democrats balk.”