Senators overrode conservative opposition to attach an amendment reviving the federal Export-Import Bank to a long-term, must-pass highway bill late Monday, hours after the House Majority Leader said the legislation was dead on arrival.

The Senate voted 64-29 to add the provision resuscitating the bank, a federal agency that underwrites loans to help foreign customers buy U.S. goods. It expired June 30 amid conservative opposition on Capitol Hill and on the presidential campaign trail.

Supporters in the business community say the bank is necessary for U.S. competitiveness, but conservatives say it amounts to corporate welfare, and their objections pushed the vote well past 10 p.m. ET.

GOP presidential candidate Sen. Ted Cruz, R-Texas, issued a statement after Monday's vote blasting what he called the "Washington Cartel" and lashing out at Senate Majority Leader Mitch McConnell, R-Ky.

"By casting votes in favor of cronyism and special interests, the Senate made clear what group matters most to them ... and the answer is not the American people," Cruz said. "Rather than keeping the promise [McConnell] made to every member of his party, he turned his back on the American people and allowed one of the worst examples of corporate welfare our nation has ever known to be resurrected from the dead."

The Senate will take another procedural vote on the bill Tuesday afternoon, with a vote on final passage likely to happen on Thursday. The developments set the House and Senate on a collision course ahead of Friday's deadline to extend authority for federal highway aid payments to states in the midst of the summer driving season.

"We're not taking up the Senate bill," House Majority Leader Kevin McCarthy, R-Calif., told reporters at the Capitol earlier Monday, adding that the Senate should instead take up the bill already passed by the House. "My best advice to the Senate is to get our highway bill moved forward," he said.

The House bill is a five-month extension of current programs while the Senate's version authorizes $350 billion in transportation programs for six years, though only three of those are paid for.

Authority for federal highway aid payments to states will expire Friday at midnight without action. At the same time, if Congress doesn't act before then the balance in the federal Highway Trust Fund is forecast to drop below a minimum cushion of $4 billion that's necessary to keep aid flowing smoothly to states.

House Republican leaders say their approach would buy them time to try to come up with a tax reform deal coveted by the White House and some leaders in both parties, and use that to pay for an even longer-term highway bill. But Senate Majority Leader Mitch McConnell, R-Ky. has said publicly and privately that such a deal will be all but impossible to achieve. He wants to move legislation now to dispense with the highway issue at least through next year's elections, give certainty to states and avoid repeated fights over the issue.

"Time is running out to get this bill through Congress. We're up against a deadline at the end of week," McConnell said on the Senate floor. "Jobs are on the line. Important infrastructure projects are too. So we have to get the job done."

Despite the dispute between the two chambers there's little expectation Congress would let the Friday deadline come and go without action, given pleas from state and local transportation agencies, the construction industry and others. One possibility is an even shorter-term extension of two months, which McCarthy was careful not to rule out and which was being openly discussed as a Plan B as Senate Republicans met late Monday.

If the House doesn't pass the Senate bill, "our fallback position is a 60-day extension, and then we hope they take up the six-year bill as soon as they come back," said Sen. John Hoeven, R-N.D.

Already the highway bill has become the vehicle for troublesome political fights over other issues -- not just the federal Export-Import Bank, which led to a nasty spat featuring Cruz, who accused McConnell of lying to him over the issue.

More Republican infighting broke out Monday, as an email surfaced from an aide to Sen. Mike Lee, R-Utah, suggesting that conservative groups should take Lee's fellow Republicans to task if they oppose him on a legislative maneuver to advance a repeal of President Barack Obama's health care law.

The move angered Republicans, and Lee sought to contain the damage, telling colleagues in a closed-door meeting that he hadn't authorized the email, according to Sen. Lindsey Graham, R-S.C. A statement from communications director Conn Carroll said Lee had personally apologized to McConnell. "This email is not how Sen. Lee does business," Carroll said.

If the House does leave Washington Thursday without taking up the Senate's highway bill, that would mean the Export-Import Bank stays dead at least until the fall, because the House version of the bill does not include it.

But McConnell is just as reluctant to take up the House's highway legislation, and the authors of the Senate's version took to the Senate floor Monday to urge McCarthy and House members to relent and act on the Senate version.

Fox News' Chad Pergram and the Associated Press contributed to this report.