By Veronica Stracqualursi, CNN

(CNN) -- Senate Minority Leader Chuck Schumer on Wednesday said Democrats won't fold to Republicans' scaled-down coronavirus relief plan, predicting their rejection of a near $500 billion measure will put pressure on GOP senators to negotiate with them and agree to a larger relief package.

"There's a good chance they feel the pressure once they see the Democrats are not going to fold to this emaciated bill, which leaves so much out. The pressure will mount on them," Schumer told CNN's John Berman Wednesday on "New Day."

Senate Republican leader Mitch McConnell announced Tuesday he would force his chamber to cast a vote "as soon as this week" on the GOP's new economic recovery plan. A GOP leadership aide told CNN that the Senate is expected to hold a procedural vote on the measure Thursday.

On CNN Wednesday, Schumer slammed the Republican bill for leaving out funding for state and local governments, which was allocated in the House's $3 trillion plan passed in May and has been the sticking point in negotiations with the White House and Republicans.

He also criticized the GOP plan for not excluding funds for food assistance for children, money for families evicted from their homes, relief for the travel industry and money for broadband in rural areas.

"Our bill meets the needs of the American people. Their bill meets the needs of a few ideologues who don't want to vote for anything, but they're feeling such pressure from the public, they have to come to the floor," Schumer told CNN, slamming the upcoming vote on the GOP measure as a "cynical act" because McConnell knows it won't pass.

Negotiations over another stimulus package broke down last month as the two parties remained deeply divided over the topline price tag.

Schumer and House Speaker Nancy Pelosi have been pushing $2.2 trillion for a new stimulus, calling on the White House and Republicans to meet them half way. But it's a price tag the White House and McConnell have rejected. In July, McConnell put forth a $1 trillion stimulus bill, but never brought it to a vote.

The new trimmed-down Republican bill unveiled this week provides a $300 federal boost for unemployment benefits through the end of the year and new relief for small businesses. The bill also forgives a $10 billion loan to the US Postal Service and includes liability protections for employers in coronavirus lawsuits. The bill would provide two years of tax credits for parents to cover costs of private and home schooling.