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Sens. Mark BegichMark BegichPerez creates advisory team for DNC transition The future of the Arctic 2016’s battle for the Senate: A shifting map MORE (D-Alaska), Mary LandrieuMary LandrieuCNN producer on new O'Keefe video: Voters are 'stupid,' Trump is 'crazy' CNN's Van Jones: O'Keefe Russia 'nothingburger' video 'a hoax' Trump posts O'Keefe videos on Instagram MORE (D-La.), Kay HaganKay HaganLinking repatriation to job creation Former Sen. Kay Hagan in ICU after being rushed to hospital GOP senator floats retiring over gridlock MORE (D-N.C.) and Harry ReidHarry ReidConservative Senate candidate calls on GOP to end filibuster Ex-Reid aide: McConnell's 'original sin' was casting ObamaCare as 'partisan, socialist takeover' GOP faces growing demographic nightmare in West MORE (D-Nev.) are all the subject of robocalls that charge "Senate Democrats think this shutdown is a game."

"They are playing politics by cutting off our veterans and their benefits. In a bi-partisan vote the House of Representatives wanted to make sure our veterans got the benefits they earned for fighting for our freedoms. But, SENATOR (XXX) won’t negotiate," the robocall script reads.

It urges listeners to call their senator and tells them to demand a vote on a measure to restore veterans' benefits in the Senate.

Another, similar robocall is running against Democratic National Committee Chairwoman Debbie Wasserman Schultz (D-Fla.), and notes that she voted against the measure.

The bill to restore veterans' benefits was one of a handful the House has passed in recent weeks as part of a Republican strategy to fund parts of the government — largely uncontroversial, bipartisan segments — at a time while the shutdown continues.

Republicans have used a number of these bills, which often receive a few dozen Democratic votes, in attacks over the past week.

Democrats, however, charge that the best solution to the shutdown would be to open the government entirely, and that the piecemeal approach requires lawmakers to inappropriately pick and choose what's significant to the American people.