Senator Roy Blunt of Missouri, a Republican who has led negotiations for his party, said Tuesday that his talks with Senator Patty Murray of Washington, a Democrat, had produced the outlines of an agreement that would provide about $1.1 billion in additional financing.
Mr. Blunt said negotiators were still discussing details, including how much money would need to be restored for work on Ebola. “I think we’re close to a plan that we think would work,” he said. “But we’d like a little more input. I’d like a little more input from the administration.”
Senator John Cornyn of Texas, the No. 2 Senate Republican, said lawmakers understood the seriousness of the Zika threat. “We made a down payment on the work on this virus based on the Ebola funds,” he said. “And we’re going to do everything that’s necessary in a responsible way to deal with this threat because we know it’s real.”
Senate Democratic leaders, including Ms. Murray, insisted on Tuesday that there was still no agreement, accused Republicans of stalling and said they were holding out for President Obama’s full request of $1.9 billion.
“There is no deal,” the Senate Democratic leader, Harry Reid of Nevada, said at a news conference, thumping his hand on the lectern. “I haven’t seen it. I don’t know who has seen it. We have an outline of it, but it’s not enough. We want $1.9 billion. That’s what it takes.”
Even if Republicans were to agree to the larger number, the Senate majority leader, Mitch McConnell of Kentucky, faces a challenge in figuring out how to package the deal so that it can win passage in the House, where hard-line conservatives have repeatedly balked at new government spending.
Nearly 400 American travelers have contracted the Zika virus, and public fears are rising as health officials warn that disease-carrying mosquitoes will soon arrive. Some states, particularly in the South, are scrambling to be ready.
“This is an emergency,” said Senator Bill Nelson of Florida, a Democrat, whose state expects to be among the first hit by the virus. As for Republicans, Mr. Nelson said, “They are not treating it like one.”
Representative Kevin McCarthy of California, a Republican and the majority leader, maintained on Tuesday that the best way to address the Zika virus was through the regular appropriations process. But he said Republicans needed to know more about the Obama administration’s plans before they could move.
“We have a number of questions that the appropriators have asked for, like what would the money be spent on this year, what is the money you need for next year, where are we on the vaccine?” he told reporters on Tuesday. “None of these have been answered.”
Mr. Earnest, the White House press secretary, dismissed such assertions.
“There’s no excuse for them having those unanswered questions when you consider that we’ve already put forward a detailed legislative proposal more than two months ago now,” he said. “We’ve already participated in 48 hearings in which questions about Zika have been raised. There have been briefings that have been convened by senior administration officials for both the House and the Senate to discuss this issue.
“So, I guess what I would say to members of Congress who say that they have questions about the administration’s Zika strategy: That ignorance is not an excuse.”
Congressional Democrats said they were certain Republicans would soon face public pressure amid rising fears about the virus. Democrats also noted that Congress had provided $5.4 billion in emergency legislation to fight Ebola in 2014, as well as more than $15 billion to fight flu epidemics in 2009 and 2005, and that in each case, there was no requirement for offsets to reduce other federal spending.
Some Senate Republicans said they were prepared to act.
“More and more of us understand we need to do something to combat the virus,” said Senator Lindsey Graham of South Carolina, a Republican who is the chairman of the appropriations subcommittee on state and foreign operations, which has some jurisdiction over the effort to fight Zika internationally and could provide additional funds.
Mr. Graham predicted that a deal would be reached by the end of the week.
With House Republicans insisting that they were still waiting for the White House to answer questions about the president’s request, House Democrats on Monday introduced their own bill, which would grant the full $1.9 billion.
Democrats said Republicans were stalling.
“While the House majority wastes time and resources with sham political ‘investigations,’ a public health crisis is spreading at home and abroad,” Representative Nita Lowey of New York, the senior Democrat on the House Appropriations Committee, said in a statement.
Mr. Reid, in a floor speech, urged swift action. “We have all seen the pictures of these babies with these small heads caused by a mosquito bite,” he said. “Sadly, the worst is on its way.”