McConnell said he expects the Congressional Budget Office will soon score the Senate's version of the bill, which continues to be negotiated behind closed doors among Republicans, a source with direct knowledge of what was discussed at the meeting told CNN.
He did not set a firm deadline for the vote, but Republicans are impatient with the lack of progress and political quicksand the bill is creating and want the Senate to either act quickly on health care or move on to other business.
"We had a good, productive meeting with President Trump, Vice President Pence, and congressional leadership," McConnell and House Speaker Paul Ryan said in a joint statement after the meeting. "The discussion focused on the continued progress of our shared legislative agenda and how we can accomplish our goals."
After weeks of discussions about how to move forward in a small working group, Republican senators were briefed at a lunch Tuesday on what their options are to repeal and replace Obamacare and warned that the time is quickly approaching for decisions to finally be made.
"The time is now," a Senate aide involved in discussions said. "We either go or we don't."
The aide said this is the natural point the chamber was bound to get to. The working group has spent several weeks tossing around ideas, but with conservatives and moderates still starkly divided on the best way to proceed, it's time for leadership to make the call.
According to Senate aides, during the meeting leadership tried to make it clear that lawmakers need to show their cards and decide if they are going to get behind repealing Obamacare -- a campaign promise that ultimately launched them to win back the majority in the House and the Senate in recent years.
"Leadership is stepping in now and making clear that this is what they all campaigned on, so they need to go now or move on," the aide said.
Senators are clearly impatient.
Sen. Lindsey Graham, a Republican from South Carolina, asked if there would be a vote on the health care bill by July 4 said "there better be."
"'Cause this is not like fine wine, it doesn't get better with age," he added with a laugh.
"We're at decision time," a congressional aide close to the health care conversation said. "Decisions have to start being made in order to get the package ready."
During their lunch Tuesday, Republicans were presented with a PowerPoint and a menu of options to overhaul Obamacare. But lawmakers emerging from the room were tight-lipped about what exactly is on the table. Key questions remain about how the GOP will phase out Medicaid expansion as well as how they will structure tax credits to help Americans purchase their health insurance under a Republican health care plan.
Sen. Dean Heller, a Republican from Nevada who is up for re-election in 2018, said he was still looking at the proposals and what he could support.
"The big print giveth. The small print taketh away. I'm waiting for the small print at this point," Heller said.
"I'm not going to go into details. There's been a lot of work done and we see where we go from here," said moderate Maine Republican Sen. Susan Collins.
Sen. Rob Portman, an Ohio Republican who has been a fierce advocate of more slowly phasing out Medicaid expansion than the House's repeal bill did, said the health care bill "needs some work still for me."
Sticking points: Medicaid, tax credits
Most members wouldn't get into details about what actually is on the table, but they were honest that there are still sticking points here that have to be resolved.
"They laid out the goals and then different ideas on how we achieve them and we are working on how to build consensus to get to the right mix on 50-plus votes," said North Dakota Sen. John Hoeven.
Lawmakers remain split over what to do about Medicaid. The House bill would eliminate enhanced federal funding for Medicaid expansion in 2020 and curtail support for the program overall. Moderates like Portman have advocated to phase out funding to cover low-income adults under Medicaid expansion more gradually. Conservatives like Pennsylvania's Pat Toomey want to shrink federal responsibility for the overall program even more that the House bill does by restructuring the growth rate for Medicaid funding.
The House plan would give states a set amount of money each year to cover their Medicaid enrollees. The funding level would increase annually based on the medical inflation rate in the Consumer Price Index, which grows more quickly than the standard inflation rate. Toomey argues that using the growth rate of medical care spending would lead to an unsustainable Medicaid program, so he advocates for tying Medicaid funding increases to the standard inflation rate instead.
Other options that are on the table include how to structure tax credits. Unlike the House's health care repeal bill, which based the tax credits mainly on age, Senate Republicans have suggested tying them to income and even geographic location in order to make health care more affordable for low-income individuals living in areas that have expensive health care costs such as Alaska and rural America.
"There should be," Republican Sen. Lisa Murkowski told reporters. "Alaska is an extreme outlier and part of it is just our geography, it's our low-density population so if there is not some kind of geographic cost adjustor it makes it tough for me."
However, adjusting the tax credits for income and geographic location would make them even more similar to Obamacare's premium subsidies, which are tax credits based on income and cost of coverage in one's area. Conservatives are sure to oppose this idea. Several, including Sen. Rand Paul of Kentucky, have said the House GOP tax credits already are too much like Obamacare's subsidies.