Senate Majority Leader Chuck Schumer (D-NY) speaks to the media during a news conference in the U.S. Capitol in Washington, U.S., January 26, 2021.Al Drago | ReutersCongress will take its first votes Tuesday on the path toward passing Democrats’ $1.9 trillion coronavirus relief package.Both the House and Senate plan to hold procedural votes on a budget resolution, which will unlock the reconciliation process. It will allow Democrats to approve rescue legislation without any Republican support.Democrats have contended they need to inject more money into the health and economic response as soon as possible. While a handful of Republicans hope to strike a smaller deal after meeting with President Joe Biden on Monday, they face a challenge in finding a middle ground between Democrats’ plan and the GOP’s $618 billion offer.”Time is a luxury our country does not have,” Senate Majority Leader Chuck Schumer, D-N.Y., said in announcing a vote to move forward with the budget process, which needs a simple majority to advance.He later added that Democrats “want this important work to be bipartisan” and would welcome input from Republicans.Democrats, who gained a narrow Senate majority last month, have made another aid package their top priority since Biden took office. They have argued the $900 billion relief law passed in December, which came after months of federal inaction that allowed millions to fall into poverty and hunger, did not go far enough to address the scale of the health and economic crises.Multiple Republicans have called for money to speed up the vaccine distribution process, buoy small businesses and provide short-term relief to unemployed Americans. GOP lawmakers have questioned the need for the level of spending backed by Biden.The Republican senators who met with Biden on Monday did not appear to make much progress toward a compromise. However, Sen. Bill Cassidy, a Louisiana Republican and part of the GOP group, is “optimistic that something can happen,” he told CNBC on Tuesday.During the meeting, Biden “expressed his hope that the group could continue to discuss ways to strengthen” the White House plan, press secretary Jen Psaki said in a statement. She said Biden reiterated “that he will not slow down work on this urgent crisis response, and will not settle for a package that fails to meet the moment.”Democrats’ proposal includes $1,400 direct payments to most Americans, a $400 per week federal jobless benefit through September, and $350 billion for state, local and tribal relief. It also puts $170 billion into K-12 schools and higher education institutions, along with $20 billion into a national vaccination program, among a slew of other provisions.The Republican offer cuts from Biden’s in major ways. Stimulus checks would be $1,000 instead of $1,400, and start to phase out at $40,000 in income for individuals rather than $75,000.It would offer $300 per week in unemployment insurance through June, $100 less weekly than in Biden’s proposal for three fewer months. It would also direct only $20 billion toward K-12 schools and not include any state, local and tribal support, which is a priority for Democrats.In criticizing the GOP proposal Monday, incoming Senate Finance Committee Chair Ron Wyden, D-Ore., pointed to the earlier cutoff of the unemployment supplement.Cassidy, meanwhile, made the case for a smaller bill in part by citing a Congressional Budget Office report anticipating the economy will recover “rapidly.” While the economy is expected to bounce back amid widespread vaccine deployment this year, 18 million people were still receiving unemployment benefits last month.The $300 per week unemployment supplement passed in December expires in mid-March.The budget resolution filed by Schumer and House Speaker Nancy Pelosi, D-Calif., includes instructions for relevant committees to draft relief policies. The measures include the direct payments, unemployment aid, Covid-19 vaccine distribution and testing funds, rental and mortgage assistance, small business support, and school funding, among others.The instructions did not include a federal $15 per hour minimum wage. Democrats support the policy, but rules governing the use of reconciliation could prevent them from passing it as part of the bill.The budget rules are just one of the hurdles Democrats face in trying to pass legislation without Republicans. They still may have to convince some skeptical Democrats, Sen. Joe Manchin of West Virginia in particular, to support the package.A bill would fail in an evenly divided Senate if any Democrats defect.Subscribe to CNBC on YouTube.