Senate Democrats plan to try to pin any failure to extend tax relief for families making less than $250,000 a year on House Republicans, after the Senate passed such a bill Wednesday.

But as they did with a popular domestic violence prevention measure, GOP lawmakers are dismissing the Democratic bill because it runs afoul of the Constitution, even though Senate Majority Leader Harry Reid (D-Nev.) tried to fix the problem.

The Senate passed Reid’s bill, 51-48, after reaching a deal to allow simple majority votes for both Republican and Democratic plans to extend the 2001 and 2003 tax cuts enacted under President George W. Bush.

The GOP plan would extend all of the expiring tax rates for one year and provide relief from some other tax provisions, as well as establish an expedited process for a tax code overhaul next year.

Retiring Sens. Jim Webb (D-Va.) and Joe Lieberman (I-Conn.) voted against both plans.

Lieberman wants to take broader action on the federal debt now.

“Just imposing across-the-board tax increases for individuals and small businesses that make over $250,000 a year is neither tax reform nor the balanced deficit-reduction agreement our country needs right now,” he said.

Senators turned back the Republican plan to extend all the tax relief by a vote of 45-54. Republicans plan to use the votes against vulnerable Democrats seeking re-election, including Sens. Claire McCaskill (Mo.) and Bill Nelson (Fla.).

Simple majority votes have become a rarity, with cloture motions or complex agreements frequently requiring support of 60 Senators to get bills passed.

Senate Minority Leader Mitch McConnell (R-Ky.) said his Conference only allowed the Democratic-favored tax bill to sail through the Senate because it was sure to die in the House, thanks to the Constitution’s “Origination Clause,” which requires revenue measures to start in the House.

“The only reason we won’t block it today is that we know it doesn’t pass constitutional muster and won’t become law. If the Democrats were serious, they’d proceed to a House-originated revenue bill as the Constitution requires,” the Kentucky Republican said.

In a bid to resolve that issue, Reid tried to get Republicans to allow him to insert the language of the Senate legislation into a House-passed tax bill. Doing so, however, could put House Republicans in a more difficult position. The procedural issue gives House leadership a good excuse to ignore the measure or return it to the Senate without action.

When the House believes the Senate is undermining its constitutional prerogative to start the process of writing tax law, the chamber’s leadership may send the bill back to the Senate with a “blue slip” attached. Alternatively, the House may just sit on the bill.

That’s what happened with the Senate version of the Violence Against Women Act reauthorization.

In that case, the Senate passed the bipartisan bill with visa fee language that House tax writers determined was an unconstitutional tax.

House Republicans have repeatedly cited the blue slip issue as the reason for delay in negotiations on the final package, but the Senate version of the VAWA reauthorization also provides new domestic violence protections for Native American tribes, illegal immigrants and the LGBT community.

Republican Sen. Lisa Murkowski (Alaska) last month signed a joint letter with Senate Judiciary Chairman Patrick Leahy (D-Vt.) to Speaker John Boehner encouraging him to call up the Senate’s bill.

Michael Steel, a spokesman for the Ohio Republican, has told reporters that the Senate should be the side of the Capitol to act first on a revised bill without the language that exposed the bill to a blue slip.

Leahy, Conference Secretary Patty Murray (Wash.) and other Democrats say the House GOP is hiding behind the constitutional explanation.

“House Republicans don’t want to talk about the fact that they are denying vulnerable communities of women the protections that the Senate VAWA bill includes,” Murray said. “So they have ducked and covered under a blue slip argument that they know has been routinely overcome. It’s a convenient argument, but they only seem to use it when it’s convenient for them.”

“The Speaker’s hands are not tied on this matter. He is choosing to hold up this bill and those efforts must stop,” Leahy said.

In fact, when lawmakers want to work around the pesky blue slips, they do. Earlier this year, the Senate passed a highway bill that would have had no chance of passing constitutional muster, because it reauthorized fuel taxes.

Nonetheless, Senators agreed by unanimous consent to insert the text into a House-passed transportation bill and set up a conference, averting a procedural standoff like the one they face on the VAWA reauthorization.

Both parties have used the blue slip workarounds to advance legislation they favor.

The House used the maneuver in 2009 under then-Speaker Nancy Pelosi (D-Calif.) to grease the wheels for tourism promotion legislation that was a top priority of Reid.