WASHINGTON (Reuters) - A long-running battle over gun control in the United States reaches a critical stage next week in the U.S. Senate amid signs Americans are more willing to accept limited restrictions after the deadliest mass shooting in modern U.S. history. While it is far from likely new measures will pass, the Orlando, Florida, gay nightclub massacre of 49 people and a suggestion by Republican presidential candidate Donald Trump that something be done have fostered a different atmosphere. While President Barack Obama was in Orlando consoling the survivors of the rampage by a gunman who claimed allegiance to Islamic State militants, the U.S. Senate moved closer to votes on limited gun control measures. About 71 percent of Americans, including eight out of 10 Democrats and nearly six out of 10 Republicans, favor at least moderate regulations and restrictions on guns, according to a Reuters/Ipsos poll conducted from Monday to Thursday. That was up from 60 percent in late 2013 and late 2014. As always, Democrats were challenging Republicans to vote for new restrictions and reject pressure from the National Rifle Association, the powerful gun lobby that has been known to punish politicians who thwart its will. U.S. Senator Chris Murphy of Connecticut and fellow Democrats set the U.S. Capitol abuzz by talking on the Senate floor for nearly 15 straight hours to demand that Congress act on gun control. They ended their speeches before dawn, citing a Republican pledge to hold votes soon on measures to expand background checks on gun buyers and to prevent people on U.S. terrorism watch lists from buying guns. The Senate is expected to vote on Monday on four proposals. One from Democrat Dianne Feinstein would let the government prevent terrorist suspects from buying guns. A second from Republican John Cornyn, the No. 2 Senate Republican, would require court approval within three days for a government ban on an individual’s attempt to buy a gun. Democrats have said Cornyn’s plan is unworkable; Republicans say Feinstein’s might harm the rights of people wrongly on terror suspect lists. A third proposal, from Democrat Murphy, would expand background check procedures to the sales of all firearms, including those online and at gun shows. A fourth proposal, from Republican Senator Chuck Grassley, would provide for law enforcement to be notified if a person investigated for terrorism in the last five years tries to buy a gun.  Gun control is a potent issue in U.S. politics. Republicans, who control the Senate, have blocked Democratic-backed gun control measures over the years, saying they infringe on the right to bear arms guaranteed by the U.S. Constitution. Any bill would have to pass both houses of Congress and be signed by the president to become law. At his weekly news conference on Thursday, Paul Ryan, speaker of the House of Representatives, injected a note of caution. “We don’t take away a citizen’s rights without due process,” said Ryan, the top U.S. elected Republican. “If you have a quick idea in the heat of the moment that says let’s take away a person’s rights without due process, we’re going to defend the Constitution.” A string of mass shootings across the United States in schoolhouses, churches, movie theaters and other public places has failed to break the deadlock. The last major gun control measure was a ban in 1994 on semi-automatic assault weapons such as the one used in Orlando on Sunday. The ban expired 10 years later. One of the most dramatic moments in the Senate debate came when Republican Senator John McCain, who is in a tough re-election race in Arizona, told reporters Obama is “directly responsible” for Islamic State-inspired attacks on Americans like the one in Orlando. He later said he meant to say he blamed Obama’s decision to withdraw most U.S. forces from Iraq, and that this had fueled the rise of Islamic State. Murphy, asked what would be the message if the Senate fails to act on the gun control measures next week, suggested it could be a campaign issue for the Nov. 8 election. “There are going to be a lot of voters in this country who are going to watch ... the votes that are cast next week,” he said. Trump, the presumptive Republican nominee for president has been endorsed by the NRA. He jumped into the gun debate by saying he would meet with NRA leaders to talk about barring people who are on terrorism watch lists from buying guns. “I’ll be looking at it very, very seriously - the terror watch list and the no-fly list, I’m going to be talking to the NRA about that and starting a real dialogue. I think a lot of people agree with me but I want to really hear what they have to say,” Trump told Fox News on Wednesday night. Democrats were deeply skeptical that Trump’s word signaled any sort of shift toward more Republican support for Democratic-backed gun control proposals. “He is going to meet with the NRA. ... What’s he going to come out saying? ‘Oh the NRA and I agreed we shouldn’t have terrorists have guns,’ but doing nothing about it,” U.S. Senator Chuck Schumer of New York told reporters.  