WASHINGTON (AP) — President Obama’s allies in the Senate stepped forward with a plan Thursday to cut $14 billion from his budget for the upcoming fiscal year. That’s double the $7 billion cut sought by House Democrats.

But Republicans on the Appropriations Committee said the cuts didn’t go far enough and opposed the idea — along with three appropriations bills for the budget year that begins in October. The panel approved the Democratic proposal on a party-line vote.

The differences between the parties are tiny when compared to the $1.14 trillion overall pot available to lawmakers writing the Cabinet agency budgets passed each year by Congress. But Republicans had staked out a position earlier this week demanding an additional $6 billion cut — a difference between the parties of just one half of 1 percent.

The GOP-proposed cuts are drawn from a bipartisan proposal by Sens. Jeff Sessions, R-Ala., and Claire McCaskill, D-Mo., that has attracted as many as 59 votes in the Senate this year. Democrats supported the cap when voting on the budget last year.

The GOP proposal would have still provided for a $10 billion increase over current spending. The Democratic plan provides for a $16 billion increase.

Obama has proposed a freeze on most domestic agency budgets, though he exempts homeland security and veterans programs. But he’s calling for an $18 billion, 3 percent increase for the Pentagon.

The Pentagon would receive a smaller budget increase in the range of 2 percent under the Senate Democratic plan.

Senate Appropriations Committee Chairman Daniel Inouye, D-Hawaii, initially proposed an $8 billion cut from Obama’s budget but upped the ante in response to GOP protests, proposing that the $6 billion additional in additional cuts come from the Pentagon budget.

‘‘It won’t hurt the Defense Department,’’ Inouye said.

Top committee Republican Thad Cochran of Mississippi said he was ‘‘attracted’’ to the idea and that it was a ‘‘fair compromise.’’ But the panel got into a confusing parliamentary tangle and Republicans, including Cochran, opposed Inouye’s split-the-difference compromise after being denied a vote on their own plan.

Senate Republican Leader Mitch McConnell of Kentucky, making a rare appearance at a committee session, opposed the Democratic compromise and GOP discipline held.

‘‘It looked to me like a compromise was about to be struck, but I think the leader decided not to agree,’’ Cochran said.

Ordinarily, the overall cap on appropriations bill — which fund the approximately one-third of the budget passed by Congress each year — would be set by Congress’ annual budget resolution. But Democrats have opted against passing a congressional budget plan, in large part because it would have put them on record backing large, intractible budget deficits.

After wrangling over the budget cap, the panel approved bills funding the departments of Agriculture, Homeland Security and Veterans Affairs, all by party-line votes. The panel has a longstanding history of bipartisanship and its GOP members typically provide crucial support to advance the measures past Republican conservatives.

Given the partisanship gripping Congress, few if any of the 12 spending bills are likely to become law before the midterm elections. That could set the stage for a massive ‘‘omnibus’’ spending bill that would pass in a lame duck session.