House Republicans are considering pairing the next debt ceiling increase with the budget resolution for fiscal 2014, which would allow the measure to pass the Senate under reconciliation.

The plan is hardly fully hatched, nor is it necessarily preferred by the GOP. And it depends largely on whether House Republicans and Senate Democrats can come to terms on a budget plan and proceed to a conference committee, which itself continues to look like a stretch. The two sides passed starkly different budget plans and have yet to figure out a path toward compromise.

But multiple Republican sources confirm that House Republicans are considering the option of including debt-ceiling-increase language in the budget resolution package, which under reconciliation rules would preclude a filibuster and allow the Senate to raise the federal borrowing limit with a vote of just 51 members. The government is due to hit the debt limit late next month, although the administration could push it to later this summer.

“There is a sense among some in the leadership ranks that a deal is possible — a fairly large deal,” said one political operative with relationships in the House. “The mechanism to get it done would be a joint budget resolution with reconciliation instructions.”

Senate reconciliation rules were intended to protect the budget resolution from being filibustered, as legislation passed under such auspices requires only 51 votes to clear. But occasionally Senate majorities have used the reconciliation rules for bills with sweeping implications beyond revenue, such as President Barack Obama’s health care overhaul, which passed according to such rules in 2010 after Scott P. Brown’s election to the Senate provided Republicans with the vote they needed to sustain a filibuster.

Asked to comment on House Republican strategy on the debt ceiling and how seriously the conference is considering running it through the budget and reconciliation process, a GOP leadership aide declined to comment. “Budget talks between House and Senate continue on both member and staff levels to find common ground for an agreement in conference.”