Senator Charles Schumer (D-NY) speaks as Senators Sheldon Whitehouse (D-RI), left, and Tom Udall (D-NM), right, listen during a news conference in the U.S. Capitol building on June 23, 2016 in Washington, DC.

Senate Democrats on Wednesday unveiled a sweeping bill to protect and expand voting access, limit big money's influence in elections and boost public officials' ethics requirements, following the passage of near-identical legislation in the House.

But even Democrats doubt that the ambitious bill stands much of a chance of making it through the Republican-held Senate led by Majority Leader Mitch McConnell, R-Ky.

The "For The People Act," introduced by Senate Minority Leader Chuck Schumer, D-N.Y., Sen. Tom Udall, D-N.M., and Sen. Jeff Merkley, D-Ore., offers a laundry list of reforms that its Democratic sponsors claim will "put power back in the hands of the American people."

Udall TWEET

The broad legislation would require states to support voter registration expansions such as same-day registration, and would crack down on illicit campaign spending by strengthening a ban on foreign money in elections and requiring political groups to disclose the names of donors who contribute more than $10,000.

It also pushes for giving Washington, D.C., "full congressional voting rights and self-government, which only statehood can provide." And in a clear shot at President Donald Trump — who broke with longstanding precedent by refusing to release his tax returns — the proposal would require that presidential and vice presidential candidates' returns be publicly disclosed by the Federal Election Commission.

Schumer, at a news event Wednesday morning, challenged the Republican majority in the Senate: "Where do they stand on dark money cascading into our system? Where do they stand on making it easier, not harder, for people to exercise their right to vote? Where do they stand on cleaning up the swamp?"

The Senate bill was introduced less than three weeks after its so-called companion legislation in the House, H.R. 1, cleared that Democrat-led chamber on a 234-193 party-line vote.

McConnell's stance on H.R. 1 suggests he will refuse to allow a vote on the Senate Democrats' bill. In a January op-ed for The Washington Post, McConnell slammed what he dubbed the "Democrat Politician Protection Act," claiming it was a "power grab" filled with "far-left proposals" and intended as "simply a naked attempt to change the rules of American politics to benefit one party."

The White House said in a statement in early March that "if H.R. 1 were presented to the President, his advisors would recommend he veto the bill."

Neither the White House nor McConnell's office immediately responded to a request for comment on the legislation.

Democrats recognize that their bill faces long odds of passage in the Senate, let alone making it past Trump's desk.

"Sen. McConnell has already indicated that he doesn't intend to bring it up," a Democratic aide familiar with the legislation told CNBC. "But we're certainly not giving up."

The aide said there was "no question" that special interest groups were "counting on McConnell to do their bidding," and admitted that "he probably will in this case again."

But, the aide added, "we're going to make him as uncomfortable as possible."