WASHINGTON — Senate Democrats intend to introduce legislation by mid-week to raise the nation’s debt limit without the type of unrelated conditions Republicans have said they intend to seek, officials said today.

The White House signaled it would accept even a brief extension in borrowing authority to prevent an unprecedented default.

The emerging measure is designed to assure no repetition of the current borrowing squeeze until after the 2014 elections.

Depending on the Republican response, it could be the middle of next week before a final vote is taken on the measure, close to the Oct. 17 deadline that Treasury Secretary Jacob Lew has set for Congress to avert a possible default.

It is unclear when Republicans in the House, who hold a majority, intend to advance debt limit legislation of their own.

Republicans have said they will seek long-term deficit cuts or reforms to benefit programs and perhaps a wholesale rollback in environmental rules as the price for raising the current $16.7 trillion debt limit. President Barack Obama has ruled out negotiations, although he has said he is willing to discuss fiscal and other issues with the GOP once the weeklong partial government shutdown is over and the Treasury is free to borrow.

Gene Sperling, a senior Obama economic adviser, was pressed on whether he would rule out a two- or three-week extension on increasing the nation’s $16.7 trillion debt limit. Lew has warned that on Oct. 17 he exhausts the bookkeeping maneuvers to keep borrowing.

“There’s no question that the longer the debt limit is extended, the greater economic certainty there will be in our economy which would be better for jobs, growth and investment,” Sperling said at a breakfast sponsored by the newspaper Politico. “That said, it is the responsibility of Congress to decide how long and how often they want to vote on doing that.”