Something unusual happened in the Senate on Tuesday, when both sides of the aisle showed a willingness to debate legislation to address a rise in violence against Asian Americans and Pacific Islanders.

The divisive partisanship of recent years has kept even popular legislation from the kind of floor action expected for the bill, starting Wednesday, including the possibility of votes on bipartisan amendments.

But Democrats cited both an urgency to address the hate crimes against AAPI individuals and the straightforwardness of the legislation by Sen. Mazie K. Hirono, D-Hawaii, as reasons to skip the typical committee process and hold a floor vote.

Senate Majority Leader Charles E. Schumer told reporters Tuesday morning that “we hope to get it done this week if we don’t have real obstruction.”

Against the backdrop of a larger debate about changing Senate rules to strip the minority party of its way to block legislation, that meant Republicans faced a dilemma of whether to take a high-profile vote to block the bill or to allow action on a priority for the Democratic majority and President Joe Biden.

“If we can’t say hate crimes against Asian Americans and others is reprehensible and ought to be punishable, that’s a serious mistake,” Senate Majority Whip Richard J. Durbin, D-Ill., told reporters.

Republicans emerged from their weekly lunch Tuesday with word that enough members of their conference would vote to allow debate on the bill, and leave it to Schumer and Minority Leader Mitch McConnell to negotiate how to navigate floor votes on amendments.

McConnell, who is married to former Transportation Secretary Elaine Chao, referenced the recent shootings of six women of Asian descent in Atlanta.

“As a proud husband of an Asian American woman, I think this discrimination is a real problem. And it preceded the murders that were recently on full display,” the Kentucky Republican told reporters. “And I’m hoping we can work out an agreement to get on the bill in a normal way, have some amendments and move to final passage.”

The measure from Hirono, among other provisions, would designate a point person at the Justice Department to expedite the review of violent hate crimes motivated by the actual or perceived relationship to the spread of COVID-19, and seek to ease reporting of such incidents.

Hirono said one of the Republican concerns was the focus on a connection between COVID-19 and the rise of these hate crimes — and that can be addressed on the floor.

“We want to make sure that everyone understood there’s a cause and effect here, but I’m open to eliminating that so that we can get to the real issue, which is the rise in hate crimes against AAPIs and what can we do about it,” Hirono said.

Connecticut Democratic Sen. Richard Blumenthal said there are “a number of amendments” for the bill that could get votes, including legislation he introduced with Kansas GOP Sen. Jerry Moran.

Blumenthal and Virginia Democratic Rep. Donald S. Beyer Jr. have pushed for years for a version of the legislation, which among other provisions would create grants for state and local governments to combat hate crimes.

“We don’t really have a vote count,” Blumenthal said. “But what we know for sure is that there is bipartisan support, better reporting, better penalties, better police support [that] is pretty noncontroversial.”

An agreement between the party leaders on amendments would help clear a path to the bill passing the Senate.

“Are there other Republican amendments besides the one I intend to offer, is one question, so what does that do to the process?” Moran said. “There’s no agreement yet, because there’s no known number of amendments.”

Schumer, after word emerged that Republicans were poised to vote to move to floor debate and offer some amendments, said the urgency drove the approach.

“If we went through committee and hearing and all that, it would take a month or two,” the New York Democrat said. “We want to have a bipartisan process. Going on the floor, and having amendments that are germane and improve the bill, change the bill in a variety of ways, is the best way to do it bipartisan because of the urgency.”

Lindsey McPherson, Katherine Tully-McManus, Rachel Oswald and Michael Macagnone contributed to this report.