In this April 4, 2017, file photo, the Capitol is seen at dawn in Washington. Bipartisan bargainers are making progress toward a budget deal to prevent a partial federal shutdown this weekend, a major hurdle overcome when President Donald Trump signaled he would put off his demand that the measure include money to build his border wall with Mexico. (AP Photo/J. Scott Applewhite, File)

WASHINGTON (AP) — Bipartisan bargainers are making progress toward a budget deal to prevent a partial federal shutdown this weekend, a major hurdle overcome when President Donald Trump signaled he would put off his demand that the measure include money to build his border wall with Mexico.

Republicans are also vetting proposed changes to their beleaguered health care bill that they hope will attract enough votes to finally push it through the House.

Both efforts come with Congress back from a two-week break just days before Trump’s 100th day in office, an unofficial measuring stick of a new president’s effectiveness. With little to show in legislative victories so far, the Trump administration would love to claim achievements on Capitol Hill by that day — this Saturday.

The same day, federal agencies would have to close unless lawmakers pass a $1 trillion spending bill financing them or legislation keeping them open temporarily while talks continue. Republicans hope to avoid the ignominy of a government shutdown while their party controls Congress and the White House.

White House spokesman Sean Spicer said Monday that administration negotiators including Trump’s budget chief, Mick Mulvaney, “feel very confident” that a shutdown won’t occur.

Democrats, whose votes are needed to pass the budget measure, had a less charitable version of negotiations. In a conference call with reporters aimed at criticizing Trump’s first 100 days as ineffective, party leaders said the biggest shutdown threat was from Trump’s demand that the spending bill include funds for the barricade along the Mexican border.

That threat appeared to be easing Monday evening when Trump told reporters from conservative media that he would be willing to return to the funding issue in September. Two people in the room described his comments to The Associated Press.

Those comments represented a retreat from just last week, when Mulvaney said getting money for Trump’s wall in the budget bill was one of the administration’s “priorities.”

Nonetheless, Trump tweeted Tuesday, “Don’t let the fake media tell you that I have changed my position on the WALL. It will get built and help stop drugs, human trafficking etc.”

House Minority Leader Nancy Pelosi, D-Calif., approved of Trump’s apparent shift. “The president’s comments this evening are welcome news given the bipartisan opposition to the wall, and the obstacle it has been to the continuing bipartisan negotiations in the appropriations committees,” she said in a statement late Monday.

Senate Minority Leader Chuck Schumer, D-N.Y., said, “It’s good for the country that President Trump is taking the wall off the table in these negotiations.” Both Democratic leaders had criticized Trump earlier Monday.

Trump had told supporters Mexico would pay for the wall, but with Mexico refusing to foot the bill he now wants Congress to make a down payment. The wall’s cost estimates range past $20 billion. Republicans are seeking an initial $1.4 billion in the spending bill.

The other major budget stumbling block involved a Democratic demand for money for insurance companies that help low-income people afford health policies under President Barack Obama’s health law, or that Trump abandon a threat to use the payments as a bargaining chip. Supporters of the health law warn its marketplaces could collapse if those funds are taken away.

Separately, the White House and congressional Republicans are gauging whether a plan to revise the GOP’s stalled health care bill would garner enough converts to rekindle hopes for House passage of the legislation.

Their initial bill would repeal some coverage requirements under Obama’s law, offer skimpier subsidies for consumers to buy care and roll back a Medicaid expansion. GOP leaders avoided a planned House vote last month, which would have failed due to opposition from GOP moderates and conservatives alike.

The proposed changes would retain several requirements imposed by Obama’s 2010 statute, including obliging insurers to cover seriously ill customers.

But states could obtain federal waivers to some of those requirements. Those include mandates that insurers charge healthy and seriously ill customers the same premiums and cover specified services like hospitalization and emergency room visits.

Supporters say the proposal is significant because it would retain guaranteed coverage for people with costly illnesses. Critics say it would effectively weaken that assurance because insurers in states getting waivers could charge sky-high rates.

Those waivers may not help win moderate support. They have opposed the underlying GOP bill because of its cuts in Medicaid and to federal subsidies Obama’s law provides many people buying individual policies.

But it might persuade conservatives who felt the earlier Republican bill didn’t erase enough of the statute, though it’s unclear it will win over enough of them to achieve House passage.

The proposed changes were negotiated by Rep. Mark Meadows, R-N.C., head of the conservative House Freedom Caucus, and Rep. Tom MacArthur, R-N.J., a leader of the centrist House Tuesday Group. Vice President Mike Pence also participated, Republicans say.

Those two groups plan to meet separately this week to consider the proposal.