FIRST ON FOX: The top Senate Republican argued that while Senate Democrats may be the ones voting against reopening the government, they're not the ones calling the shots.Senate Majority Leader John Thune, R-S.D., told Fox News Digital in an interview that as the Department of Homeland Security (DHS) shutdown continues, it's Democrats' voters who are pushing them to continue blocking funding for the agency."The Democrats up here on the Hill are so afraid of their far-left base," Thune said. "And I think the far-left base, their demand right now, is defund ICE, defund law enforcement, which is not, by any stretch, a reasonable position."The agency has been shut down for 35 days, putting the latest closure into record-breaking territory. Senate Democrats have, so far, blocked four attempts to reopen the agency over demands for stringent reforms to Immigration and Customs Enforcement (ICE) and how agents operate in the field.THUNE ACCUSES CRITICS OF 'CREATING FALSE EXPECTATIONS' AMID BACKLASH OVER STALLED SAVE AMERICA ACTNegotiations had ground to a halt for several weeks, with Senate Minority Leader Chuck Schumer, D-N.Y., and his caucus staying quiet on the latest offer from the White House.That communication breakdown began to thaw this week when Democrats responded with an offer the White House dubbed unserious. And signs of a deal further improved on Thursday when a handful of Democratic negotiators sat down for the first time with Senate Republicans and border czar Tom Homan.It also comes as lines at airports stretch for several blocks as workers go unpaid, and concerns of terrorist attacks are at a fever pitch in the wake of the Iran war. Thune will again put a bill to reopen the agency on the floor on Friday, and Democrats are again expected to block it.REPUBLICANS SIGNAL NO RETREAT ON SAVE ACT AS MARATHON SENATE DEBATE KICKS OFFStill, Thune said that the meeting "suggested even more movement" toward breaking the funding logjam but remained wary of Democrats actually wanting to make a deal to end the shutdown.He also noted that until Thursday, Democrats had consistently rejected Republicans’ offers to get into a room and hash it out, and he contended that it was the White House making their offers to Democrats public that likely spurred the latest confab."My impression is, at least up until now, that the edict has gone out from the paternalistic Democrat fathers that none of their children should be talking to Republicans about how to solve this problem in a way that gets them actual reforms in place," Thune said, "and funds an important department that has a number of agencies that are really critical, not only to national security, but to emergency management and other things."DEMS UNMOVED AS WHITE HOUSE REVEALS DHS CONCESSIONS IN SHUTDOWN BATTLE"So it seems to me, at least they are — these guys — they are running scared," he continued. "They, I think, believe they benefit politically from this."Several Democrats left the meeting with Homan and Sens. Susan Collins, R-Maine, and Katie Britt, R-Ala., declining to comment on the discussion. When asked if lawmakers were any closer to a deal, Sen. Patty Murray, D-Wash., said, "No."Still, Republicans were hopeful that there would soon be a breakthrough to the impasse."Unfortunately, the Democrats' list of demands keeps growing and growing, and that makes it difficult," Collins said. "But the group that was in there is operating in good faith, and I hope we'll get together again very soon."