House Minority Whip Steny H. Hoyer is urging his Democratic colleagues to vote against a debt ceiling measure on the House floor Wednesday, potentially making it more difficult for Republicans to pass the bill.

Still, Democratic lawmakers in marginal districts are being told they are free to vote how they need to, according to a Democratic leadership aide.

The “no budget, no pay” provision in the debt ceiling bill is similar to a proposal offered by Rep. Jim Cooper of Tennessee that a good number of his fellow Democrats co-sponsored in the 112th Congress, making it difficult for those lawmakers to oppose it now.

On Tuesday, Hoyer ripped the bill as a “gimmick” that is “probably unconstitutional” and “worthy of almost unrestrained derision.”

With 233 members, Republicans can ill afford to lose votes if they are attempting to reach 218 votes on their own. The GOP is mostly united around this bill, but is expecting some defections, so even a handful of Democrats voting for the measure could determine whether it passes the House.

Hoyer announced that he was working against the vote late Tuesday in an email to colleagues with the subject line: “WHIP ALERT – DEMOCRATS ARE URGED TO VOTE NO ON H.R. 325 – NO BUDGET, NO PAY AT OF 2013.”

The email said, “This bill is not a serious proposal by House Republicans,” and ended with a restatement, in all capital letters, “DEMOCRATS ARE URGED TO VOTE NO ON H.R. 325.”

Hoyer’s office says it is not formally whipping the vote.