By Siobhan Hughes 

WASHINGTON--Senate Democrats rejected on Monday a GOP bid to open negotiations on competing House and Senate versions of legislation to fund the Department of Homeland Security, leaving Republicans with dwindling options in their attempts to use the legislation to block President Barack Obama's immigration policies.

The 47-43 vote fell short of the 60 needed for passage and put an end to what House Republicans had portrayed as their main hope for salvaging legislation that includes language preventing the implementation of orders providing millions of illegal immigrants a temporary reprieve from deportation.

The Senate on Friday passed a funding bill without those provisions after Democrats blocked consideration of the House bill several times.

In a separate vote, the Senate sent its original bill back to the House, which Republican conservatives had rejected just days earlier. Majority Leader Mitch McConnell (R., Ky.) and Sen. John Cornyn (R., Texas), the No. 2 Senate Republican, were among those voting in favor.

The pair of Monday votes heightens pressure on House Speaker John Boehner (R., Ohio) to accept the Senate's version of the bill, which would fund the department through Sept. 30, the end of fiscal 2015. The department's funding is set to expire on Friday under a one-week extension passed last week.

Democrats and some Republicans predict that the House will ultimately hold a vote this week on the Senate's measure to fund homeland security.

A spokesman for Mr. Boehner said in a statement that "we are disappointed that Senate Democrats have once again rejected regular order. Now, we will talk with House Republican members about the way forward."

House Rules Committee Chairman Pete Sessions (R., Texas) said he expected the House would "dispose of" the matter this week, and suggested that the immigration fight is likely to be out of the hands of Congress.

"We're going to count on the judges," Mr. Sessions said. A federal judge in Texas last month temporarily blocked Mr. Obama's immigration actions, saying they should have been issued in accordance with the Administrative Procedure Act. The Obama administration has appealed that ruling.

A budget fight this early in a new Congress is the result of unfinished business from last year, when Republicans deferred action on homeland-security money while agreeing to fund the rest of the government through fiscal 2015.

Then as now, Republicans, especially in the House, were furious over Mr. Obama's decision to give some four million illegal immigrants the chance to apply for work permits and a temporary reprieve from deportation. Mr. Obama also expanded a similar 2012 program for young people brought to the U.S. as children.

Republicans feel that Mr. Obama ignored not just Congress but also voters, who rejected Democrats in the 2014 midterm elections and gave Republicans their biggest House majority in decades.

Separately on Monday, the Internal Revenue Service confirmed it would allow illegal immigrants benefiting from Mr. Obama's actions to file for tax refunds for prior years, fueling an outcry from Republicans.

The IRS explanation came in a letter from Commissioner John Koskinen to Sen. Charles Grassley (R., Iowa). In response, Mr. Grassley vowed to push legislation to overturn the policy.

The action allows many to obtain work permits and Social Security numbers, which in turn would allow those who qualify to apply for a tax break known as the Earned Income Tax Credit, the IRS said. The credit provides cash payments to lower-income households, even those that didn't earn enough to pay income tax, and can be worth several thousand dollars.

John D. McKinnon contributed to this article.

Write to Siobhan Hughes at siobhan.hughes@wsj.com