WASHINGTON — President Barack Obama is hosting top House Republicans to seek an opening in an impasse that has shuttered much of the government and threatens a catastrophic federal default.

The White House meeting, set for today, comes as House GOP leaders are contemplating advancing a short-term debt limit increase designed to calm jittery stock and bond markets and allow more time to untie the knot that has the government partially shut down for a 10th day and facing a first-ever default between Oct. 17 and the end of the month.

A short-term debt limit measure was expected to be a topic at a closed-door House GOP meeting this morning. It wasn’t clear what conditions GOP leaders might seek to attach to the bill, if any, but conservatives consistently have been pushing top Republicans like Speaker John Boehner to add conditions beyond what Obama says he’ll accept.

Also, Treasury Secretary Jacob Lew was heading to Capitol Hill today to both give and get a public scolding.

Lew’s appearance before the Senate Finance Committee promised to be yet another public restatement of the administration’s stance that Congress needs to reopen the government and lift the U.S. borrowing cap before Obama will negotiate over the nation’s budget ills.

The game of Washington chicken over increasing the debt limit — required so Treasury can borrow more money to pay the government’s bills in full and on time — already has sent the stock market south, spiked the interest rate for one-month Treasury bills and prompted Fidelity Investments, the nation’s largest manager of money market mutual funds, to sell federal debt that comes due around the time the nation could hit its borrowing limit.

Wednesday featured lots of activity but no progress toward ending the budget and debt limit impasses.

Obama had House Democrats over to the White House, while Republican conservatives heard a pitch from the House Budget Committee chairman, Rep. Paul Ryan, R-Wis., on his plan to extend the U.S. borrowing cap for four to six weeks while jump-starting talks on a broader budget deal that could replace cuts to defense and domestic agency budgets with cuts to benefit programs like Medicare and reforms to the loophole-cluttered tax code. Curbs to “Obamacare” were not mentioned.

At the White House, Obama told House Democratic loyalists that he still would prefer a long-term increase in the nation’s $16.7 trillion borrowing cap but said he’s willing to sign a short-term increase to “give Boehner some time to deal with the tea party wing of his party,” said Rep. Peter Welch, D-Vt.

A midday meeting Wednesday between the two top House Republicans and Democrats, meanwhile, yielded no progress. Rival aides to Boehner and Democratic leader Nancy Pelosi of California even disagreed over who asked for the meeting.

Obama invited the entire House GOP to the White House today but Boehner opted to send a smaller squadron of about 20 mostly senior members.