Manchin urged lawmakers to read the 49-page proposal. He said it should dispel any misconceptions about infringing on the constitutional right to bear arms.
The senators' agreement actually includes language expanding firearms rights by easing some restrictions on transporting guns across state lines, protecting sellers from lawsuits if buyers passed a check but later used a gun in a crime and letting gun dealers conduct business in states where they don't live.
"If you are a law-abiding gun owner, you're going to like this bill," Manchin said.
He acknowledged the vote would be tight. Asked how many votes he thought he had now, Manchin said: "Well, we're close. We need more."
The compromise, if successful, would be added to broader gun control legislation to strengthen laws against illegal gun trafficking and to increase slightly school security aid.
Other additions to the legislation also are expected to be debated this week, including a measure that would allow concealed hand gun permits issued by one state to be accepted nationwide as a de facto background check.
Sen. Marco Rubio, R-Fla., said in news show interviews that concealed weapons permits should be applied nationally. He also called for more prosecution of people that are trying to buy guns and fail a background check.
The Senate is also expected to consider, and reject, Democratic amendments to ban assault weapons and ammunition magazines carrying more than 10 rounds.
Manchin and Toomey were on CNN's "State of the Union" and CBS' "Face the Nation." McCain was on CNN.