WASHINGTON (AP) — A Democratic senator who supports rolling back some of the financial rules put in place after the 2008 financial crisis warned bankers Tuesday that the legislation will stall if it comes back to the Senate for another vote.

Sen. Mark Warner's comments are a warning shot to House Republicans, who are insisting on adding to Senate-passed legislation that would scale back the law known as Dodd-Frank.

The Virginia senator told members of the American Bankers Association that 16 Democrats and one independent who voted for the Senate bill have taken "an awful lot of heat" for a bill he said has been mischaracterized by some members of his own party. In other words, they're not anxious to revisit the debate.

"This bill will not pass if it comes back to the Senate," Warner said. "We stretched this about as far as we can go. The House of Representatives needs to accept this legislation."

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The Senate passed legislation in March targeting relief for all but the biggest banks. The House had earlier passed a more expansive bill that also went after the Consumer Financial Protection Bureau. The House version passed with no Democratic support.

Warner's comments came in a speech to bankers attending the trade group's annual conference in Washington. GOP leaders in the House have insisted that their members be allowed to add to the Senate bill measures that have received bipartisan support in the House.

James Ballentine, an executive vice president at the ABA, told bankers at the conference that he believes a Dodd-Frank rollback will happen.

"It will be soon and very soon that we think this legislation will move forward," Ballentine said.

But ABA officials also warned the bankers that the legislative calendar is growing short, and that's why the group has urged House leaders to take up the Senate bill. Ballentine said members of the House want to get more done to provide relief for banks, but "the appetite to get some more done is not there in the Senate at this time."

Rep. Blaine Luetkemeyer, R-Mo., told the bankers that he believes the Senate will eventually acquiesce to the House's demands and said the "Senate is real good at rhetoric."

He said the House has the ability to make it a better bill by adding provisions with broad bipartisan support.

"If it's controversial, let's take it out because we don't want to kill the bill," he said.

Still, Luetkemeyer would not offer a firm timeline to the bankers for when he thought a final vote could occur but said he hoped it could occur before the August recess. He warned that if the House did not push back and get more of what its members want, then the Senate would make similar take-it-or-leave-it demands with other bills during the remainder of this congressional session.

"We'll have to take every single bill that they send us," Luetkemeyer said. "That means the whole system is going to be reliant on the Senate. We can't have that."