An agreement could be announced as early as Tuesday.
Efforts to tackle politically-charged immigration issues and rapidly rising health insurance premiums appeared to be faltering.
Capitol Hill Democrats rejected a White House bid to extend protections for so-called Dreamer immigrants in exchange for $25 billion in funding for a wall on the U.S.-Mexico border. Democrats appeared likely to yield on $1.6 billion in wall funding, Trump's official request for the 2018 budget year, but they were digging in against Trump's plans to hire hundreds of new immigration agents.
A dispute over abortion seemed likely to scuttle a Senate GOP plan to provide billions in federal subsidies to insurers to help curb health insurance premium increases.
Sen. Mitch McConnell, R-Ky., was working on Trump's behalf against funding for a Hudson River tunnel and rail project that's important to Senate Minority Leader Chuck Schumer, D-N.Y., and Republicans from New York and New Jersey.
Monday's developments were described by several lawmakers - as well as congressional aides in both parties who spoke on condition of anonymity because the talks remain secretive.
House and Senate action is needed by midnight Friday to avert another government shutdown.
The bill would implement last month's budget agreement, providing 10 percent increases for the Pentagon and domestic agencies. Coupled with last year's tax cuts, it heralds the return of trillion-dollar budget deficits as soon as the budget year starting in October.
Many battles over policy riders were sorted out in marathon negotiations over the weekend. As is typical, many of the policy issues were melting away.
"We've had at least 100 that we've taken out," said Vermont Sen. Patrick Leahy, top Democrat on the Appropriations Committee.
For instance, an effort to add a plan to revive federal subsidies to stabilize the individual health insurance market and help the poor cover out-of-pocket costs under President Barack Obama's health law appeared to be failing. A complicated dispute involving abortion was at fault.
Trump told Sens. Lamar Alexander, R-Tenn., and Susan Collins, R-Maine, that he supports addressing the health insurance issue now as part of the catchall spending plan.
Alexander and Collins are seeking to revive payments to insurers, which Trump halted last fall, that reimburse the carriers for reducing out-of-pocket costs for many low-earning customers. Those reductions are required by the Obama health law, and insurers have made up for the lost federal payments by boosting premiums.
The Republicans said their subsidy plan would reduce premiums by up to 40 percent over time. They would also create a $30 billion, three-year reinsurance program that states could use to help insurers afford to cover their most seriously ill, expensive consumers.
Democrats, however, oppose GOP provisions that would forbid the federal payments from being used to help pay for insurance policies that provide abortion.
And Republicans appeared likely to fail in a bid to fix a glitch in the recent tax bill that subsidizes grain sales to cooperatives at the expense of for-profit grain companies, several aides said.
"We need to fix that problem," said House Majority Leader Kevin McCarthy, R-Calif.
Elsewhere, efforts to use the measure as a vehicle to extend protections for young immigrants under the Deferred Action for Childhood Arrival, or DACA, program appeared likely to fail, lawmakers and aides said. Trump killed the Obama-era program in September, but a court decision has essentially left it in place, for now. The White House had revived the idea in recent days - offering on Sunday a 30-month extension of DACA protections in exchange for $25 billion for Trump's border wall - but Democrats demanded protections for a broader pool of immigrants than had signed up for DACA, a request denied by GOP negotiators.
"Nobody's really moved," said No. 2 Senate Republican John Cornyn of Texas.
Trump tweeted Monday night: "The Democrats do not want to help DACA. Would be so easy to make a deal!"
The president, meanwhile, has privately threatened to veto the whole package if a $900 million payment is made on the Hudson River Gateway Project, a priority for Schumer. Trump's opposition is alarming Northeastern Republicans such as Rep. Peter King of New York, who lobbied Trump on the project at a St. Patrick's luncheon in the Capitol Thursday.
The Gateway Project would add an $11 billion rail tunnel under the Hudson River to complement deteriorating, century-old tunnels that are at risk of closing in a few years. It enjoys bipartisan support among key Appropriations panel negotiators on the omnibus measure who want to get the expensive project on track while their coffers are flush with money.
Associated Press writer Alan Fram contributed to this report.
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