Updated, 7:24 p.m.: As of the end of the day, McCaskill says 53 senators have signed the letter.

Sen. Claire McCaskillClaire Conner McCaskillDemocrats criticize Medal of Freedom for Limbaugh as 'slap in the face' Kansas City, Kan., responds to Trump tweet: We root for the Chiefs, too Trump mocked for Super Bowl tweet confusing Missouri for Kansas MORE (D-Mo.) said Wednesday she has half the Senate on board with her effort to end senators' anonymous holds on nominations.

McCaskill said she now had 50 senators who had signed the letter she has been circulating pledging to end the use of the practice, in which one senator can object, without giving his or her name, to any nominee moving forward.

McCaskill tweeted Wednesday:

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Now have 50 signatures on End the Secret Hold letter.More work on it today.Rules being broken by failure of Rs to reveal who's holding noms.

McCaskill said, too, in a conference call with Missouri reporters Wednesday that she's hopeful she can win a 60-vote, filibuster-proof majority on reform.

"We've crossed the majority -- we haven't gotten to 60, yet I'm feeling confident that we will get to 60," she said.

The Missouri centrist has been leading the charge against the practice, arguing it has been used to some effect by Republicans in the minority to stall or stop President Barack ObamaBarack Hussein ObamaEx-CIA chief calls Trump intel shakeup a 'virtual decapitation' of the intelligence community Five takeaways from new fundraising reports for 2020 Democrats Obama sends birthday wishes to John Lewis: 'Thanks for making good trouble' MORE's nominees.

Senate Majority Leader Harry ReidHarry Mason ReidReid pushes back on Sanders suggestion that a Democrat with plurality of delegates should be the nominee Harry Reid on 'Medicare for All': 'Not a chance in hell it would pass' The Hill's Morning Report - Sanders on the rise as Nevada debate looms MORE (D-Nev.) railed against the practice of secret holds on Tuesday, suggesting the matter might be referred to the Senate Ethics Committee at some point.

Updated at 12:58 p.m.