By Carlo Muñoz - 09/22/13 03:35 PM EDT
As congressional lawmakers barrel toward a Senate showdown over ObamaCare and a possible government shutdown, one Senate Republican is predicting that cooler heads will eventually prevail on Capitol Hill.
Sen. Amy Klobuchar (D-Minn.) agreed with Lee's assumption, adding, "the last thing the American people want now is [Congress] playing political games" with the country's fiscal well-being.
"[Political] brinkmanship ... is not the way to go," she said in an interview Sunday on NBC.
Their comments come as Lee and Sen. Ted Cruz (R-Texas) are rallying support among Senate Republicans ahead of a crucial vote next week on a House spending bill to continue government funding into the next fiscal year, beginning in October.
House GOP members on Friday approved legislation to defund ObamaCare as part of plan to avoid a government shutdown next month.
"Republicans are committed to solving the problem" of excessive government spending, beginning with the repeal of ObamaCare, Rep. Marsha Blackburn (R-Tenn.) said during the same show.
"As much as the president wants a [government] shutdown, he is not going to get it," she added.
Lee said GOP backers of the House measure "have support in the Senate" to defund ObamaCare.
Senate Republicans are now attempting to peel off several red state Democrats to reinforce the GOP minority in the upper chamber.
"We have seen Americans rallying around the idea" of eliminating the controversial health care plan, Lee said Sunday.
Senate Majority Leader Harry Reid (D-Nev.) has said Democrats will block any attempt to push through the House-passed funding measure through the Senate.
Senate Republicans on Monday will begin eyeing amendments and a possible cloture vote to the Senate version of legislation to avoid a government shutdown, according to Cruz.